What is the answer to log_{x}(0.01)=-2 ?

The answer to log_{x}(0.01)=-2 is x=10

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log_{x}(0.01)=-2

lo g_{x} (0.01) = - 2

x = 10

Solution steps

lo g_{x} (0.01) = - 2

Apply log rules

\frac{1}{lo g _{0.01} ( x )} = - 2

Multiply both sides by

lo g_{0.01} (x)

\frac{1}{lo g _{0.01} ( x )} lo g_{0.01} (x) = - 2 lo g_{0.01} (x)

Apply log rules

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

lo g_{2} (n) = 1 0^{6}

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

lo g_{3} (x + 4) + lo g_{3} (4 x - 7) = 3

0.81 = lo g_{10} (x)

lo g_{2} (3 \cdot 2^{x} - 4) = 2 x - 1