What is the answer to log_{x}(1/27)=-3 ?

The answer to log_{x}(1/27)=-3 is x=3

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log_{x}(1/27)=-3

lo g_{x} (\frac{1}{27}) = - 3

x = 3

Solution steps

lo g_{x} (\frac{1}{27}) = - 3

Apply log rules

\frac{ln ( \frac{1}{27} )}{ln ( x )} = - 3

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{27} )}{ln ( x )} ln (x) = - 3 ln (x)

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

8 x^{2} = 64 x lo g_{2} (x)

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

(ln (x))^{2} - 2 ln (x) - 3 = 0

x, ln (x) = ln (y) + c

lo g_{10} (x + 9) - lo g_{10} (x) = 3