What is the answer to log_{x}(16)=-2 ?

The answer to log_{x}(16)=-2 is x= 1/4

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log_{x}(16)=-2

lo g_{x} (16) = - 2

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

lo g_{x} (16) = - 2

Apply log rules

\frac{1}{lo g _{16} ( x )} = - 2

Multiply both sides by

lo g_{16} (x)

\frac{1}{lo g _{16} ( x )} lo g_{16} (x) = - 2 lo g_{16} (x)

Simplify

1 = - 2 lo g_{16} (x)

Switch sides

- 2 lo g_{16} (x) = 1

Divide both sides by

- 2

lo g_{16} (x) = - \frac{1}{2}

Apply log rules

x = \frac{1}{4}

Verify Solutions:

x = \frac{1}{4}

True

The solution is

x = \frac{1}{4}

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

lo g_{10} (7) + lo g_{10} (x - 4) = 1

lo g_{100} (x) = \frac{1}{2}

lo g_{2} (x + 3) = 2

- 5 + 2 ln (3 x) = 5