What is the answer to log_{x}(8)=-3 ?

The answer to log_{x}(8)=-3 is x= 1/2

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log_{x}(8)=-3

lo g_{x} (8) = - 3

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

lo g_{x} (8) = - 3

Apply log rules

\frac{1}{lo g _{8} ( x )} = - 3

Multiply both sides by

lo g_{8} (x)

\frac{1}{lo g _{8} ( x )} lo g_{8} (x) = - 3 lo g_{8} (x)

Simplify

1 = - 3 lo g_{8} (x)

Switch sides

- 3 lo g_{8} (x) = 1

Divide both sides by

- 3

lo g_{8} (x) = - \frac{1}{3}

Apply log rules

x = \frac{1}{2}

Verify Solutions:

x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

lo g_{10} (3 x) = 3

lo g_{2} (x) + lo g_{2} (2 x - 7) = 2

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

ln (x) + ln (x - 7) = 0

lo g_{3} (x) = 9