What is the answer to log_{x}(100)=-3 ?

The answer to log_{x}(100)=-3 is x= 1/(\sqrt[3]{100)}

Solve for x: log_{x}(100)=-3

The solution is x= 1/(\sqrt[3]{100)}

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lo g_{x} (100) = - 3

x = \frac{1}{3 100}

Decimal

x = 0.21544 \dots

Solution steps

lo g_{x} (100) = - 3

Apply log rules

\frac{1}{lo g _{100} ( x )} = - 3

Multiply both sides by

lo g_{100} (x)

\frac{1}{lo g _{100} ( x )} lo g_{100} (x) = - 3 lo g_{100} (x)

Simplify

1 = - 3 lo g_{100} (x)

Switch sides

- 3 lo g_{100} (x) = 1

Divide both sides by

- 3

lo g_{100} (x) = - \frac{1}{3}

Apply log rules

x = \frac{1}{3 100}

Verify Solutions:

x = \frac{1}{3 100}

True

The solution is

x = \frac{1}{3 100}

ln (13 x) + 1 = 0

lo g_{10} (2 x) + lo g_{10} (3) = lo g_{10} (30)

lo g_{10} (x) = 10

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

ln (4 x) = 2 x

What is the answer to log_{x}(100)=-3 ?
The answer to log_{x}(100)=-3 is x= 1/(\sqrt[3]{100)}
Solve for x: log_{x}(100)=-3
The solution is x= 1/(\sqrt[3]{100)}