What is the answer to log_{x}(16)=-1 ?

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

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log_{x}(16)=-1

lo g_{x} (16) = - 1

x = \frac{1}{16}

Decimal Notation

x = 0.0625

Solution steps

lo g_{x} (16) = - 1

Apply log rules

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

Multiply both sides by

lo g_{16} (x)

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

Simplify

1 = - lo g_{16} (x)

Move

lo g_{16} (x)

to the left side

1 + lo g_{16} (x) = 0

Move

1

to the right side

lo g_{16} (x) = - 1

Apply log rules

x = \frac{1}{16}

Verify Solutions:

x = \frac{1}{16}

True

The solution is

x = \frac{1}{16}

lo g_{x} (\frac{1}{36}) = - 2

lo g_{0.3} (x) = 2

lo g_{3} (x - 8) + lo g_{3} (x) = 2

5 ln (5 x - 8) + 5 = 30

x, lo g_{x} (y) = z