What is the answer to log_{-b}(64)=2 ?

The answer to log_{-b}(64)=2 is b=-8

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log_{-b}(64)=2

lo g_{- b} (64) = 2

b = - 8

Solution steps

lo g_{- b} (64) = 2

Apply log rules

\frac{1}{lo g _{64} ( - b )} = 2

Multiply both sides by

lo g_{64} (- b)

\frac{1}{lo g _{64} ( - b )} lo g_{64} (- b) = 2 lo g_{64} (- b)

Simplify

1 = 2 lo g_{64} (- b)

Switch sides

2 lo g_{64} (- b) = 1

Divide both sides by

2

lo g_{64} (- b) = \frac{1}{2}

Apply log rules

- b = 8

Solve

- b = 8 : b = - 8

b = - 8

Verify Solutions:

b = - 8

True

The solution is

b = - 8

lo g_{10} (x) = - 5.6

lo g_{10} (x) = - 5.7

lo g_{10} (x) = - 5.4

lo g_{10} (x) = - 5.1

lo g_{a} (2) = \frac{1}{2}