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calculus online - Free exercises and solutions to help you succeed!

Logarithm Rules – Exercise 5574

Exercise

Solve the equation:

\log_x (\frac{1}{27})=3

Final Answer

x=\frac{1}{3}

Solution

Using Logarithm Rules we get:

\log_x (\frac{1}{27})=3

-\log_x 27=3

-\log_x 3^3=3

-3\log_x 3=3

\log_x 3=-1

x^{-1}=3

\frac{1}{x}=3

x=\frac{1}{3}

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