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Solution assignment 06 Exponential equations

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Assignment 6

Solve:

5(\displaystyle\frac{1}{5})^{x+4}=25(5^2)

Solution

We can write this equation as:

5(\displaystyle\frac{1}{5})^{x+4}=25(5^2)

(\displaystyle\frac{1}{5})^{x+4}=5(5^2)

(5^{-1})^{x+4}=5^3

5^{-x-4}=5^3

Thus:

-x-4=3

x=-7

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