02.03.2022

Solve the equation algebraically. 2lnx + 7 = ln(4x) + 10

Round your final answers to two decimal places.

. 0

Step-by-step answer

09.07.2023, solved by verified expert

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Mathematics
Step-by-step answer
P Answered by Master

x = 80.34 (2 dp)

Step-by-step explanation:

2\ln(x)+7=\ln(4x)+10

\implies \ln(x^2)+7=\ln(4x)+10

\implies \ln(x^2)-\ln(4x)=10-7

\implies \ln\left(\dfrac{x^2}{4x}\right)=3

\implies \ln\left(\dfrac{x}{4}\right)=3

\implies e^{\ln\left(\dfrac{x}{4}\right)}=e^3

\implies \dfrac{x}{4}=e^3

\implies x=4e^3

\implies x=80.34 \textsf{ (2 dp)}

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Mathematics
Step-by-step answer
P Answered by PhD

Area of rectangle= L*b

here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

Mathematics
Step-by-step answer
P Answered by PhD

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3

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