What is the answer to log_{x}(81)= 4/3 ?

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

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log_{x}(81)= 4/3

lo g_{x} (81) = \frac{4}{3}

x = 27

Solution steps

lo g_{x} (81) = \frac{4}{3}

Apply log rules

\frac{1}{lo g _{81} ( x )} = \frac{4}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{81} (x) \cdot 4

Simplify

3 = lo g_{81} (x) \cdot 4

Switch sides

lo g_{81} (x) \cdot 4 = 3

Divide both sides by

4

lo g_{81} (x) = \frac{3}{4}

Apply log rules

x = 27

Verify Solutions:

x = 27

True

The solution is

x = 27

ln (x) - 1 = 0

lo g_{5} (2 x - 23) = lo g_{5} (x - 5)

8 n^{2} = 64 n lo g_{2} (n)

lo g_{10} (x) = 0.4

0.24 = lo g_{10} (x)