What is the answer to log_{x}(9)= 1/3 ?

The answer to log_{x}(9)= 1/3 is x=729

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log_{x}(9)= 1/3

lo g_{x} (9) = \frac{1}{3}

x = 729

Solution steps

lo g_{x} (9) = \frac{1}{3}

Apply log rules

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

Simplify

3 = lo g_{9} (x)

Apply log rules

729 = x

Switch sides

x = 729

Verify Solutions:

x = 729

True

The solution is

x = 729

0 = ln (2 x)

20 lo g_{10} (g) = 30

2 lo g_{4} (x) - 5 = 12 lo g_{x} (4)

ln (4 x + 3) = 1

ln (4 x + 3) = 2