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Solution assignment 07 Logarithmic equations

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Assignment 7

Solve:

\ln(2-x)=1+\ln(x)

Solution

The domains of the \ln-functions are subsequently:

2-x>0 and x>0

or:

0<x<2

We rewrite the equation as follows:

\ln(2-x)=\ln(e)+\ln(x)

\ln(2-x)=\ln(ex)

2-x=ex

x=\displaystyle\frac{2}{e+1}

This solution lies in the domain and is valid.

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