2 Answers

Yoni Mayer · Answer 1 · 2022-01-20T09:53:29+0000

Answer:

x=4

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

Giannis Mp · Answer 2 · 2022-01-24T12:08:59+0000

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
.

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