What is the answer to log_{x}(4)= 2/3 ?

The answer to log_{x}(4)= 2/3 is x=8

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log_{x}(4)= 2/3

lo g_{x} (4) = \frac{2}{3}

x = 8

Solution steps

lo g_{x} (4) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{4} ( x )} = \frac{2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{4} (x) \cdot 2

Simplify

3 = lo g_{4} (x) \cdot 2

Switch sides

lo g_{4} (x) \cdot 2 = 3

Divide both sides by

2

lo g_{4} (x) = \frac{3}{2}

Apply log rules

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

a, lo g_{a} (b) = 3

lo g_{x} (64) = 4

lo g_{6} (x) + lo g_{6} (x - 1) = 1

lo g_{x} (16) = \frac{2}{3}

lo g_{5} (2 x + 3) = lo g_{5} (3)