What is the answer to log_{x}(6)= 1/3 ?

The answer to log_{x}(6)= 1/3 is x=216

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log_{x}(6)= 1/3

lo g_{x} (6) = \frac{1}{3}

x = 216

Solution steps

lo g_{x} (6) = \frac{1}{3}

Apply log rules

\frac{1}{lo g _{6} ( 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_{6} (x) \cdot 1

Simplify

3 = lo g_{6} (x)

Apply log rules

216 = x

Switch sides

x = 216

Verify Solutions:

x = 216

True

The solution is

x = 216

ln (3 x - 15) = 5

ln (3 x - 15) = 3

3 ln (8 x - 10) + 15 = 6

lo g_{3} (x + 7) + lo g_{3} (x + 8) = 8

lo g_{10} (x) + lo g_{10} (4 x) = 2