Question

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

Answer 1

Answer:

The value of x is about 2.206.

Step-by-step 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.