What is the answer to log_{b}(81)=4 ?

The answer to log_{b}(81)=4 is b=3

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log_{b}(81)=4

lo g_{b} (81) = 4

b = 3

Solution steps

lo g_{b} (81) = 4

Apply log rules

\frac{1}{lo g _{81} ( b )} = 4

Multiply both sides by

lo g_{81} (b)

\frac{1}{lo g _{81} ( b )} lo g_{81} (b) = 4 lo g_{81} (b)

Simplify

1 = 4 lo g_{81} (b)

Switch sides

4 lo g_{81} (b) = 1

Divide both sides by

4

lo g_{81} (b) = \frac{1}{4}

Apply log rules

b = 3

Verify Solutions:

b = 3

True

The solution is

b = 3

lo g_{10} (x) - lo g_{10} (8) = 1

lo g_{4} (1.5 x) = lo g_{16} (3 x - 1)

lo g_{k} (4) = 2

lo g_{10} (3 x) + lo g_{10} (x) 9 = 3

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