What is the answer to log_{x}(0.001)=3 ?

The answer to log_{x}(0.001)=3 is x=0.1

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log_{x}(0.001)=3

lo g_{x} (0.001) = 3

x = 0.1

Solution steps

lo g_{x} (0.001) = 3

Apply log rules

\frac{1}{lo g _{0.001} ( x )} = 3

Multiply both sides by

lo g_{0.001} (x)

\frac{1}{lo g _{0.001} ( x )} lo g_{0.001} (x) = 3 lo g_{0.001} (x)

Simplify

1 = 3 lo g_{0.001} (x)

Switch sides

3 lo g_{0.001} (x) = 1

Divide both sides by

3

lo g_{0.001} (x) = \frac{1}{3}

Apply log rules

x = 0.1

Verify Solutions:

x = 0.1

True

The solution is

x = 0.1

lo g_{2} (x^{2} - 9 x + 4) = 2

ln (x) = 1 - x

lo g_{2 x} (3 x^{2} + 10 x - 16) = 2

lo g_{0.3} (x) = - 2

lo g_{x} (0.05) = - 2

What is the answer to log_{x}(0.001)=3 ?
The answer to log_{x}(0.001)=3 is x=0.1
Solve for x: log_{x}(0.001)=3
The solution is x=0.1