Question

What is the true solution to the equation below?

l n e Superscript l n x Baseline + l n e Superscript l n x squared Baseline = 2 l n 8
x = 2

Answer 1

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

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`.