What is the answer to log_{b}(27)= 3/4 ?

The answer to log_{b}(27)= 3/4 is b=81

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log_{b}(27)= 3/4

lo g_{b} (27) = \frac{3}{4}

b = 81

Solution steps

lo g_{b} (27) = \frac{3}{4}

Apply log rules

\frac{1}{lo g _{27} ( b )} = \frac{3}{4}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 4 = lo g_{27} (b) \cdot 3

Simplify

4 = lo g_{27} (b) \cdot 3

Switch sides

lo g_{27} (b) \cdot 3 = 4

Divide both sides by

3

lo g_{27} (b) = \frac{4}{3}

Apply log rules

b = 81

Verify Solutions:

b = 81

True

The solution is

b = 81

lo g_{10} (x) = x

0.55 = ln (x)

ln (y) = 1

9 = lo g_{10} (x)

lo g_{5} (x + 2) = 1 + lo g_{5} (x - 2)