Question

Solving Exponential and Logarithmic Equations In Exercise, solve for x.
2 In x + In(x - 2) = 0

Answer 1

The value of x is about 2.206.

Explanation:

Consider the given equation is

`2\ln x+\ln (x-2)=0`

We need to find the value of x.

Using the properties of logarithm we get

`\ln x^2+\ln (x-2)=0`
`[\because \ln a^b=b\ln a]`

`\ln (x^2(x-2))=0`
`[\because \ln (ab)=\ln a+\ln b]`

`\ln (x^2(x-2))=ln 1`
`[\because \ln 1=0]`

On comparing both sides we get

`x^2(x-2)=1`

`x^3-2x^2=1`

Using graphing calculator, the real solution of the above equation is

`x\approx 2.206`

Therefore, the value of x is about 2.206.