What is the answer to log_{x}(125)=-3 ?

The answer to log_{x}(125)=-3 is x= 1/5

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log_{x}(125)=-3

lo g_{x} (125) = - 3

x = \frac{1}{5}

Decimal Notation

x = 0.2

Solution steps

lo g_{x} (125) = - 3

Apply log rules

\frac{1}{lo g _{125} ( x )} = - 3

Multiply both sides by

lo g_{125} (x)

\frac{1}{lo g _{125} ( x )} lo g_{125} (x) = - 3 lo g_{125} (x)

Simplify

1 = - 3 lo g_{125} (x)

Switch sides

- 3 lo g_{125} (x) = 1

Divide both sides by

- 3

lo g_{125} (x) = - \frac{1}{3}

Apply log rules

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

ln (x) + ln (x - 2) = 1

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

lo g_{\frac{3}{4}} (x) = 2

3 lo g_{9} (x) = (lo g_{3} (x))^{2}

lo g_{4} (x) + lo g_{4} (x + 6) = 2