What is the answer to log_{x}(27)= 3/2 ?

The answer to log_{x}(27)= 3/2 is x=9

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log_{x}(27)= 3/2

lo g_{x} (27) = \frac{3}{2}

x = 9

Solution steps

lo g_{x} (27) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{27} ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{27} (x) \cdot 3

Simplify

2 = lo g_{27} (x) \cdot 3

Switch sides

lo g_{27} (x) \cdot 3 = 2

Divide both sides by

3

lo g_{27} (x) = \frac{2}{3}

Apply log rules

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

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

lo g_{10} (c) = 10

lo g_{10} (2 x) = 4

lo g_{4} (x) = 1

lo g_{9} (x^{2} - 10) = 1