What is the answer to log_{b}(81)=2 ?

The answer to log_{b}(81)=2 is b=9

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log_{b}(81)=2

lo g_{b} (81) = 2

b = 9

Solution steps

lo g_{b} (81) = 2

Apply log rules

\frac{1}{lo g _{81} ( b )} = 2

Multiply both sides by

lo g_{81} (b)

\frac{1}{lo g _{81} ( b )} lo g_{81} (b) = 2 lo g_{81} (b)

Simplify

1 = 2 lo g_{81} (b)

Switch sides

2 lo g_{81} (b) = 1

Divide both sides by

2

lo g_{81} (b) = \frac{1}{2}

Apply log rules

b = 9

Verify Solutions:

b = 9

True

The solution is

b = 9

lo g_{10} (x^{2} - 16 x + 1) = 0

2 ln (3 x^{2} + 1) = 13

ln (15 - 2 x) = 2 ln (x)

1 = 3 lo g_{10} (4 x + 10)

lo g_{6} (9 x) - 2 lo g_{6} (2) = 3