Question

What is the true solution to the equation below?

Answer 1

Answer:

x=4

Step-by-step explanation:

What is the true solution to the equation below?

ln e Superscript ln x Baseline + ln e Superscript ln x squared Baseline = 2 ln 8

x = 2

x = 4

x = 8

Answer 2

Given:

The equation is:

$\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8$

To find:

The solution for the given equation.

Solution:

We have,

$\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8$

It can be written as:

$\ln x+\ln x^2=2\ln 8$              $[\because \ln e^x=x]$

$\ln (x\cdot x^2)=2\ln 8$              $[\because \ln a+\ln b=\ln (ab)]$

$\ln (x^3)=\ln 8^2$         $[\because \ln x^n=n\ln x ]$

On comparing both sides, we get

$x^3=8^2$

$x^3=64$

Taking cube root, we get

$x=\sqrt[3]{64}$

$x=4$

Therefore, the required solution is $x=4$.