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Solution assignment 07 Exponential equations

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Assignment 7

Solve:

3(\displaystyle\frac{1}{4})^{3x-2}=27

Solution

We can write this equation as:

(\displaystyle\frac{1}{4})^{3x-2}=9

(4^{-1})^{3x-2}=9

4^{-(3x-2)}=9

The right-hand side cannot be written as a power of 4 and thus we use logarithms:

\log(4^{-(3x-2)})=\log(9)

-(3x-2)\log(4)=\log(9)

x=\displaystyle\frac{2}{3}-\displaystyle\frac{\log(9)}{3\log(4)}

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