What is the answer to log_{x}(16)=-4 ?

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

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log_{x}(16)=-4

lo g_{x} (16) = - 4

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

lo g_{x} (16) = - 4

Apply log rules

\frac{1}{lo g _{16} ( x )} = - 4

Multiply both sides by

lo g_{16} (x)

\frac{1}{lo g _{16} ( x )} lo g_{16} (x) = - 4 lo g_{16} (x)

Simplify

1 = - 4 lo g_{16} (x)

Switch sides

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

Divide both sides by

- 4

lo g_{16} (x) = - \frac{1}{4}

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

ln (x^{2}) = 4

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

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

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

ln (5 - 2 x) = - 3