What is the answer to log_{x}(1/5)=-1 ?

The answer to log_{x}(1/5)=-1 is x=5

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log_{x}(1/5)=-1

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

x = 5

Solution steps

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

Apply log rules

\frac{ln ( \frac{1}{5} )}{ln ( x )} = - 1

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{5} )}{ln ( x )} ln (x) = - 1 \cdot ln (x)

Apply log rules

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{2} (x^{2} + 3 x - 3) = 0

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

x, ln (u) = - ln (x)

lo g_{10} (x) = - 4.7

lo g_{3} (x) = 2 lo g_{9} (6) - lo g_{9} (12)