What is the answer to log_{x}(1/32)=-5 ?

The answer to log_{x}(1/32)=-5 is x=2

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log_{x}(1/32)=-5

lo g_{x} (\frac{1}{32}) = - 5

x = 2

Solution steps

lo g_{x} (\frac{1}{32}) = - 5

Apply log rules

\frac{ln ( \frac{1}{32} )}{ln ( x )} = - 5

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{32} )}{ln ( x )} ln (x) = - 5 ln (x)

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

20 lo g_{10} (x) = - 6

lo g_{5} (125 x) = 4

lo g_{2} (6 x + 5) = 3

20 lo g_{10} (x) = 14

x, lo g_{4} (x) = 3