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}

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}

ln (5 x - 4) = ln (8) - ln (x - 2)

lo g_{10} (x) = \frac{- 1}{n}

ln (\frac{x ^{2}}{x + 2}) = 0

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

- 0.04 = lo g_{10} (x)