Solution assignment 09 Logarithmic equations

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Assignment 9

Solve:

\log_2(x)+\log_2(x-2)=3

Solution

The domain is:

x>0 and x>2

thus:

x>2

We write the equation as follows:

\log_2(x)+\log_2(x-2)=\log_2(8)

\log_2[(x(x-2)]=\log_2(8)

x(x-2)=8

x^2-2x-8=0

(x-4)(x+2)=0

The solutions of this equation are:

x=-2 or x=4

The second solution lies in the domain and is valid. The first solution lies outside the domain and does not satisfy the equation.

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