What is the answer to log_{x}(625)=-4 ?

The answer to log_{x}(625)=-4 is x= 1/5

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log_{x}(625)=-4

lo g_{x} (625) = - 4

x = \frac{1}{5}

Decimal Notation

x = 0.2

Solution steps

lo g_{x} (625) = - 4

Apply log rules

\frac{1}{lo g _{625} ( x )} = - 4

Multiply both sides by

lo g_{625} (x)

\frac{1}{lo g _{625} ( x )} lo g_{625} (x) = - 4 lo g_{625} (x)

Simplify

1 = - 4 lo g_{625} (x)

Switch sides

- 4 lo g_{625} (x) = 1

Divide both sides by

- 4

lo g_{625} (x) = - \frac{1}{4}

Apply log rules

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

lo g_{9} (2 x) - lo g_{3} (2) = 1

lo g_{3} (4 x - 2) = 4

lo g_{2} (x) = 10000000

0.83 = ln (y)

lo g_{10} (γ) = 0.16096