What is the answer to log_{x}(64)= 3/2 ?

The answer to log_{x}(64)= 3/2 is x=16

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log_{x}(64)= 3/2

lo g_{x} (64) = \frac{3}{2}

x = 16

Solution steps

lo g_{x} (64) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{64} ( 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_{64} (x) \cdot 3

Simplify

2 = lo g_{64} (x) \cdot 3

Switch sides

lo g_{64} (x) \cdot 3 = 2

Divide both sides by

3

lo g_{64} (x) = \frac{2}{3}

Apply log rules

x = 16

Verify Solutions:

x = 16

True

The solution is

x = 16

0.82 = lo g_{10} (x)

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

lo g_{b} (8) = \frac{3}{2}

x, ln (x^{2} + 4 y^{2}) = 0

lo g_{x} (x + 6) = 2