What is the answer to log_{a}(5)=-2 ?

The answer to log_{a}(5)=-2 is a= 1/(sqrt(5))

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log_{a}(5)=-2

lo g_{a} (5) = - 2

a = \frac{1}{5}

Decimal Notation

a = 0.4472135955

Solution steps

lo g_{a} (5) = - 2

Apply log rules

\frac{1}{lo g _{5} ( a )} = - 2

Multiply both sides by

lo g_{5} (a)

\frac{1}{lo g _{5} ( a )} lo g_{5} (a) = - 2 lo g_{5} (a)

Simplify

1 = - 2 lo g_{5} (a)

Switch sides

- 2 lo g_{5} (a) = 1

Divide both sides by

- 2

lo g_{5} (a) = - \frac{1}{2}

Apply log rules

a = \frac{1}{5}

Verify Solutions:

a = \frac{1}{5}

True

The solution is

a = \frac{1}{5}

lo g_{3} (x + 4) = lo g_{3} (1 - x)

lo g_{x} (\frac{1}{6}) = - 1

lo g_{7} (6 - 2 t) = 2

ln (ln (x)) = 3

lo g_{2} (\frac{3 x + 1}{4 x - 3}) = 3

What is the answer to log_{a}(5)=-2 ?
The answer to log_{a}(5)=-2 is a= 1/(sqrt(5))
Solve for a: log_{a}(5)=-2
The solution is a= 1/(sqrt(5))