What is the answer to log_{x}(1/49)=-2 ?

The answer to log_{x}(1/49)=-2 is x=7

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log_{x}(1/49)=-2

lo g_{x} (\frac{1}{49}) = - 2

x = 7

Solution steps

lo g_{x} (\frac{1}{49}) = - 2

Apply log rules

\frac{ln ( \frac{1}{49} )}{ln ( x )} = - 2

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{49} )}{ln ( x )} ln (x) = - 2 ln (x)

Apply log rules

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

lo g_{10} (x - 3) = 2 - lo g_{10} (5)

3 ln (2) + ln (x - 1) - ln (x) = ln (7)

lo g_{9} (x^{2}) = 9

lo g_{6} (x^{2} - 5 x) = 1

lo g_{10} (16 x) - lo g_{10} (4) = 2