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3241004551 [841]
3 years ago
5

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

Mathematics
1 answer:
Pani-rosa [81]3 years ago
6 0

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.

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