Mathematics : asked on jasjoh39p0rp6i

30.11.2021

If (5^1/5)^5 = 25^x, then x = ?

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09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

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x = 1/2

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)^c = a^(bc)

__

(5^(1/5))^5 = 25^x . . . . given

5^(1/5×5) = (5^2)^x . . . . simplify left side, rewrite right side

5^1 = 5^(2x) . . . . . . . . . simplify further

1 = 2x . . . . . . . . . . . . . equate exponents of the same base

x = 1/2 . . . . . . . . . . . divide by 2

_____

Additional comment

The Order of Operations tells you that exponentiation must be evaluated before multiplication or division. That means 5^1/5 is evaluated as ...

(5^1)/5 = 5/5 = 1

If you want a fractional exponent, it must be put in parentheses: 5^(1/5). If you type your expression into the Go.ogle calculator, it will strictly adhere to the Order of Operations.

If (5^1/5)^5 = 25^x, then x = ?, №18010079, 30.11.2021 22:01

If (5^1/5)^5 = 25^x, then x = ?, №18010079, 30.11.2021 22:01

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Mathematics

If (5^1/5)^5 = 25^x, then x = ?

Step-by-step answer

P Answered by Specialist

x = 1/2

Step-by-step explanation:

The applicable rule of exponents is ...

(a^b)^c = a^(bc)

__

(5^(1/5))^5 = 25^x . . . . given

5^(1/5×5) = (5^2)^x . . . . simplify left side, rewrite right side

5^1 = 5^(2x) . . . . . . . . . simplify further

1 = 2x . . . . . . . . . . . . . equate exponents of the same base

x = 1/2 . . . . . . . . . . . divide by 2

_____

Additional comment

The Order of Operations tells you that exponentiation must be evaluated before multiplication or division. That means 5^1/5 is evaluated as ...

(5^1)/5 = 5/5 = 1

If you want a fractional exponent, it must be put in parentheses: 5^(1/5). If you type your expression into the Go.ogle calculator, it will strictly adhere to the Order of Operations.

If (5^1/5)^5 = 25^x, then x = ?

If (5^1/5)^5 = 25^x, then x = ?

Mathematics

For each sentence below, find the value of x that makes each sentence true. 1) (5^1/5)^5 = 25^x x = 2) (8^1/3)^2 = 4^x x =

Step-by-step answer

P Answered by PhD

9

1)

(5^1/5)^5 = 25^(1/2) = 5

x =1/2

2) (8^1/3)^2 = 4^1 = 4

x = 1

Mathematics

For each sentence below, find the value of x that makes each sentence true. (5 ^1/5) ^5 = 25^x x = (8 ^1/3) ^2 = 4^ x x = ^a1

Step-by-step answer

P Answered by PhD

16

ANSWER

1. $x=\frac{1}{2}$

2. x=1

QUESTION 1

The first sentence is $(5^{\frac{1}{5}})^5=25^x$ .

Recall that;

$(a^m)^n=a^{mn}$

We simplify the left hand side by applying this property to get;

$5^{\frac{1}{5}\times 5}=25^x$ .

$\Rightarrow 5^{1}=25^x$ .

We now rewrite the right hand side too in an index form to obtain;

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$ .

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$ .

QUESTION 2

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

2^2=4^x

We now rewrite the left hand side too in index form to obtain;

$2^2=2^{2x}$

We equate the exponents to get;

2=2x

This implies that;

1=x

or

x=1

Mathematics

For each sentence below, find the value of x that makes each sentence true. (5 1/5) 5 = 25 x x = (8 1/3) 2 = 4 x x =

Step-by-step answer

P Answered by PhD

26

Hey!

I'll brake down every step (these steps wont have words, but if need any help, drop a comment)... And show you all the work, hope this helps...

Fractions Simplified

5 (1/5) > 26/5 > 5.2

8 (1/3) > 25/3 > 8.3333

First Problem

(5 1/5) 5 = 25x; x = ?

(5.2)*5 = 25x; x = ?

26 = 25x; x = ?

x = 26/25

x = 1.04

Second Problem

(8 1/3) 2 = 4x; x = ?

(8.3333)*2 = 4x; x = ?

16.66666 = 4x; x = ?

x = 16.66666/4

x = 4.166666

Estimated: x = 4.1667

Mathematics

For each sentence below, find the value of x that makes each sentence true. (5 ^1/5) ^5 = 25^x x = (8 ^1/3) ^2 = 4^ x x = ^a1

Step-by-step answer

P Answered by PhD

16

ANSWER

1. $x=\frac{1}{2}$

2. x=1

QUESTION 1

The first sentence is $(5^{\frac{1}{5}})^5=25^x$ .

Recall that;

$(a^m)^n=a^{mn}$

We simplify the left hand side by applying this property to get;

$5^{\frac{1}{5}\times 5}=25^x$ .

$\Rightarrow 5^{1}=25^x$ .

We now rewrite the right hand side too in an index form to obtain;

$\Rightarrow 5^{1}=5^{2x}$

We now equate the exponents to get;

$\Rightarrow 1=2x$ .

$\Rightarrow \frac{1}{2}=x$

$\Rightarrow x=\frac{1}{2}$ .

QUESTION 2

The second sentence is $(8^{\frac{1}{3}})^2=4^x$

We simplify the left hand side first to get;

$(2^{3\times \frac{1}{3}})^2=4^x$

2^2=4^x

We now rewrite the left hand side too in index form to obtain;

$2^2=2^{2x}$

We equate the exponents to get;

2=2x

This implies that;

1=x

or

x=1

Mathematics

If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)? one-fifth (one-fifth x + 5) + 5 One-fifth (5 x minus 25) + 5 StartFraction 1 Over (one-fifth x + 5) EndFraction 5 (one-fifth x + 5) + 5

Step-by-step answer

P Answered by PhD

14

The expression used to represent g(x) as inverse of f(x) is $\frac{1}{5}(5x-25)+5$

Option B is correct.

Step-by-step explanation:

We are given:

$f(x)= 5x-25\\g(x)=\frac{1}{5}x+5$

We need to find the expression that could be used to verify g(x) is the inverse of f(x).

We know that g(f(x))=x is inverse of function

So placing value of f(x) in g(x)

$g(f(x))=\frac{1}{5}(5x-25)+5$

So, the expression used to represent g(x) as inverse of f(x) is $\frac{1}{5}(5x-25)+5$

Option B is correct.

We can also solve to prove that g(f(x))=x

$g(f(x))=\frac{1}{5}(5x-25)+5\\g(f(x))=\frac{5}{5}(x-5)+5\\g(f(x))=x-5+5\\g(f(x))=x$

Mathematics

If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)? one-fifth (one-fifth x + 5) + 5 One-fifth (5 x minus 25) + 5 StartFraction 1 Over (one-fifth x + 5) EndFraction 5 (one-fifth x + 5) + 5

Step-by-step answer

P Answered by Specialist

3

$f(x)=\dfrac{2x+5}{7}\\\\
y=\dfrac{2x+5}{7}\\
7y=2x+5\\
2x=7y-5\\
x=\dfrac{7y-5}{2}\\
\boxed{f^{-1}(x)=\dfrac{7x-5}{2}}$

Mathematics

The table and graph show that there are 32 ounces in a quart. Conversion between Quarts and Ounces Ounces (x) Quarts (y) 8 0.25 16 0.5 32 1 40 1.25 On a coordinate plane, the x-axis is labeled Ounces and the y-axis is labeled quarts. The line goes through points (8, 0.25) and (16, 0.5). Which statement about the graph is true? The number of quarts is the independent variable, and the number of ounces is the dependent variable. The point (56, 1.75) is on the line. The number of ounces is graphed on the y-axis, and the number of quarts is graphed

Step-by-step answer

P Answered by PhD

21

The point (56, 1.75) is on the line.

Step-by-step explanation:

Given two points, we can get the slope (m) as follows:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the points. Replacing with (8, 0.25) and (16, 0.5):

m = (0.5 - 0.25)/(16 - 8) = 0.03125

The point-slope form of a line is:

y - y1 = m(x - x1)

Replacing with data:

y - 0.25 = 0.03125(x - 8)

To know if point (56, 1.75) is on the line, we have to replace x = 56 in the obtained equation and check y-value, as follows:

y - 0.25 = 0.03125(56 - 8)

y - 0.25 = 1.5

y = 1.5 + 0.25 = 1.75

Then, the point is on the line. This means that there are 56 ounces in 1.75 quarts.

Mathematics

The table and graph show that there are 32 ounces in a quart. Conversion between Quarts and Ounces Ounces (x) Quarts (y) 8 0.25 16 0.5 32 1 40 1.25 On a coordinate plane, the x-axis is labeled Ounces and the y-axis is labeled quarts. The line goes through points (8, 0.25) and (16, 0.5). Which statement about the graph is true? The number of quarts is the independent variable, and the number of ounces is the dependent variable. The point (56, 1.75) is on the line. The number of ounces is graphed on the y-axis, and the number of quarts is graphed

Step-by-step answer

P Answered by PhD

21

The point (56, 1.75) is on the line.

Step-by-step explanation:

Given two points, we can get the slope (m) as follows:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the points. Replacing with (8, 0.25) and (16, 0.5):

m = (0.5 - 0.25)/(16 - 8) = 0.03125

The point-slope form of a line is:

y - y1 = m(x - x1)

Replacing with data:

y - 0.25 = 0.03125(x - 8)

To know if point (56, 1.75) is on the line, we have to replace x = 56 in the obtained equation and check y-value, as follows:

y - 0.25 = 0.03125(56 - 8)

y - 0.25 = 1.5

y = 1.5 + 0.25 = 1.75

Then, the point is on the line. This means that there are 56 ounces in 1.75 quarts.

Mathematics

Which set represents the range of the function shown? (5 points) {(−1, 5), (2, 8), (5, 3), (13, −4)} a {−1, 2, 5, 13} b {−4, 3, 5, 8} c {(5, −1), (8, 2), (3, 5), (−4, 13)} d {−4, −1, 2, 3, 5, 5, 8, 13} Question 2 (5 points) (03.01 LC) Given that h(x) = 3x − 19, find the value of x that makes h(x) = 71. (5 points) a 30 b 43 c 52 d 194 Question 3 (5 points) (03.02 MC) Given the function g(x) = −3x + 4, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values. (5 points) a The value of g(−2) is smaller than

Step-by-step answer

P Answered by PhD

1

1) b. {−4, 3, 5, 8}
2) a. 30
3) d. The value of g(−2) is larger than the value of g(4).
4) b. − 1 over 2
5) d. y = −2x − 1
6) a. line through the points 0 comma 6 and 12 comma 0
7) a. It is increasing during the time interval 4 < x < 7 hours.
8) from x15 to x 25 is 4 - -16 = -20 degree change
25-15 = 10000 feet
-20/10=-2 degrees every 1000 feet.
9) Suppose that the function f(x) is the parrent function and the graph of the function g(x)=f(x)-a can be obtained from the graph of the parrent function f(x) by shifting down a units.
Rewrite the expression for the function in the following way:
g(x)=32x-9=32x+8-8-9=32x+8-17=f(x)-17.
This shows that the shift down is made by 17 units.
10) b. The graph of y = f(x) will shift down 9 units.
11) b. y + 1 = 5(x + 2)
12) c. f(x) = 2x + 5
13) b. y = 9
14) d. vertical line through the point 5 comma 0

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