What is the answer to log_{x}(0.0001)=-4 ?

The answer to log_{x}(0.0001)=-4 is x=10

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log_{x}(0.0001)=-4

lo g_{x} (0.0001) = - 4

x = 10

Solution steps

lo g_{x} (0.0001) = - 4

Apply log rules

\frac{1}{lo g _{0.0001} ( x )} = - 4

Multiply both sides by

lo g_{0.0001} (x)

\frac{1}{lo g _{0.0001} ( x )} lo g_{0.0001} (x) = - 4 lo g_{0.0001} (x)

Simplify

1 = - 4 lo g_{0.0001} (x)

Switch sides

- 4 lo g_{0.0001} (x) = 1

Divide both sides by

- 4

lo g_{0.0001} (x) = - \frac{1}{4}

Apply log rules

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

lo g_{x} (32) = \frac{5}{3}

lo g_{5} (3 x + 1) = - 2

lo g_{10} (x + 1) + lo g_{10} (2) = lo g_{10} (5 x)

lo g_{10} (3 x) = x - 1

lo g_{x + 1} (x^{2} - 3 x + 1) = 1

What is the answer to log_{x}(0.0001)=-4 ?
The answer to log_{x}(0.0001)=-4 is x=10
Solve for x: log_{x}(0.0001)=-4
The solution is x=10