What is the answer to log_{x}(9)= 2/3 ?

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

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log_{x}(9)= 2/3

lo g_{x} (9) = \frac{2}{3}

x = 27

Solution steps

lo g_{x} (9) = \frac{2}{3}

Apply log rules

\frac{1}{lo g _{9} ( 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_{9} (x) \cdot 2

Simplify

3 = lo g_{9} (x) \cdot 2

Switch sides

lo g_{9} (x) \cdot 2 = 3

Divide both sides by

2

lo g_{9} (x) = \frac{3}{2}

Apply log rules

x = 27

Verify Solutions:

x = 27

True

The solution is

x = 27

lo g_{x} (5 x - 6) = 2

ln (x) - ln (\frac{1}{x}) = 2

lo g_{4} (x) = - \frac{1}{2}

lo g_{7} (x + 9) + lo g_{7} (49) = 4

lo g_{3} (x) = 6