What is the answer to log_{x}(25)=-2 ?

The answer to log_{x}(25)=-2 is x= 1/5

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log_{x}(25)=-2

lo g_{x} (25) = - 2

x = \frac{1}{5}

Decimal Notation

x = 0.2

Solution steps

lo g_{x} (25) = - 2

Apply log rules

\frac{1}{lo g _{25} ( x )} = - 2

Multiply both sides by

lo g_{25} (x)

\frac{1}{lo g _{25} ( x )} lo g_{25} (x) = - 2 lo g_{25} (x)

Simplify

1 = - 2 lo g_{25} (x)

Switch sides

- 2 lo g_{25} (x) = 1

Divide both sides by

- 2

lo g_{25} (x) = - \frac{1}{2}

Apply log rules

x = \frac{1}{5}

Verify Solutions:

x = \frac{1}{5}

True

The solution is

x = \frac{1}{5}

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

6 + lo g_{3} (- 4 x) = 9

lo g_{3} (x^{2} - 3 x - 1) = 0

lo g_{2} (x - 5) = 3 - lo g_{2} (x - 7)

ln (x) + ln (x - 1) = ln (6)