Logarithm Rules – Exercise 5574

Exercise

Solve the equation:

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

Final Answer

Show final answer

Solution

Using Logarithm Rules we get:

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

$-\log_x 27=3$

$-\log_x 3^3=3$

$-3\log_x 3=3$

$\log_x 3=-1$

$x^{-1}=3$

$\frac{1}{x}=3$

$x=\frac{1}{3}$