27.08.2021

Solve for x 64^x^2 = 256^x

. 0

Step-by-step answer

09.07.2023, solved by verified expert
Unlock the full answer

x = 0, 1.333333...

Step-by-step explanation:

1) Convert both sides to the same base.

Solve for x 64^x^2 = 256^x, №18010346, 27.08.2021 20:34

2) Cancel the base of 16  on both sides.

Solve for x 64^x^2 = 256^x, №18010346, 27.08.2021 20:34

3) Move all terms to one side.

Solve for x 64^x^2 = 256^x, №18010346, 27.08.2021 20:34

4) Factor out the common term x.

Solve for x 64^x^2 = 256^x, №18010346, 27.08.2021 20:34

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...

It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by Specialist

x = 0, 1.333333...

Step-by-step explanation:

1) Convert both sides to the same base.

16^{1.5x^{2} } =16^{2x}

2) Cancel the base of 16  on both sides.

1.5x^{2} =2x

3) Move all terms to one side.

1.5x^{2} -2x=0

4) Factor out the common term x.

x(1.5x-2)=0

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...

Mathematics
Step-by-step answer
P Answered by PhD
64^{x-2}=256^{2x}\\ \\(4^3)^{x-2}=(4^4)^{2x}\\ \\4^{3x-6}=4^{8x}\ \ \ \ \Leftrightarrow\ \ \ \ 3x-6=8x\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x-8x=6\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -5x=6\ \ \ \ \Leftrightarrow\ \ \ \ x=- \frac{6}{5}
Mathematics
Step-by-step answer
P Answered by PhD
X^2 + 16x + ?
a^2 + 2ab + b
(a + b)^2 which is a perfect square.

To find b to determine the last value, you divide 16x by 2x.
so:
b = 8
the last value would be 8^2 which is 64.

Hence answer is C - 64
Mathematics
Step-by-step answer
P Answered by PhD
X^2 + 16x + ?
a^2 + 2ab + b
(a + b)^2 which is a perfect square.

To find b to determine the last value, you divide 16x by 2x.
so:
b = 8
the last value would be 8^2 which is 64.

Hence answer is C - 64
Mathematics
Step-by-step answer
P Answered by Specialist
To find the perfect square of an equation, you just take your "middle" term (in this case, 16), divide it by 2, then square it.

16/2 = 8
8^2 = 64

your perfect square is 64. you can check it really quick by trying to factor x^2 + 16x + 64 and seeing that it breaks down perfectly into (x + 8)(x + 8), which can be written as (x + 8)^2, showing that you have a binomial with a perfect square!!

Try asking the Studen AI a question.

It will provide an instant answer!

FREE