Solution assignment 03 Logarithmic equations

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Assignment 3

Solve:

\log(\displaystyle\frac{x+1}{x})=1

Solution

The domain of the function in the left-hand side is defined by:

\displaystyle\frac{x+1}{x}>0

and is equal to:

x>0 or x<-1

We rewrite the equation as:

\log(\displaystyle\frac{x+1}{x})=\log(10)

or:

\displaystyle\frac{x+10}{x}=10

Cross-multiplication yields:

x+1=10x

x=\displaystyle\frac{1}{9}

This solution lies in the domain and is valid.

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