What is the answer to log_{x}(128)=-7 ?

The answer to log_{x}(128)=-7 is x= 1/2

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log_{x}(128)=-7

lo g_{x} (128) = - 7

x = \frac{1}{2}

Solution steps

lo g_{x} (128) = - 7

Apply log rules

\frac{1}{lo g _{128} ( x )} = - 7

Multiply both sides by

lo g_{128} (x)

\frac{1}{lo g _{128} ( x )} lo g_{128} (x) = - 7 lo g_{128} (x)

Simplify

1 = - 7 lo g_{128} (x)

Switch sides

- 7 lo g_{128} (x) = 1

Divide both sides by

- 7

lo g_{128} (x) = - \frac{1}{7}

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

x, ln (x) = y + a

x, ln (x) = y + c

9 lo g_{10} (1 - 5 x) = 3

\frac{x}{ln ( x + 9 )} = 1

\frac{ln ( x )}{x} + (4 x)^{- 1} = 0.2