What is the answer to log_{b}(16)=-4 ?

The answer to log_{b}(16)=-4 is b= 1/2

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log_{b}(16)=-4

lo g_{b} (16) = - 4

b = \frac{1}{2}

Decimal

b = 0.5

Solution steps

lo g_{b} (16) = - 4

Apply log rules

\frac{1}{lo g _{16} ( b )} = - 4

Multiply both sides by

lo g_{16} (b)

\frac{1}{lo g _{16} ( b )} lo g_{16} (b) = - 4 lo g_{16} (b)

Simplify

1 = - 4 lo g_{16} (b)

Switch sides

- 4 lo g_{16} (b) = 1

Divide both sides by

- 4

lo g_{16} (b) = - \frac{1}{4}

Apply log rules

b = \frac{1}{2}

Verify Solutions:

b = \frac{1}{2}

True

The solution is

b = \frac{1}{2}

lo g_{10} (5 x) = 6

lo g_{7} (x^{2} - x + 1) = 1

0 = (ln (x))^{2}

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

lo g_{10} (16 x) - lo g_{10} (2) = lo g_{10} (32)