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

The answer to log_{x}(3)= 1/6 is x=729

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log_{x}(3)= 1/6

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

x = 729

Solution steps

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

Apply log rules

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Simplify

6 = lo g_{3} (x)

Apply log rules

729 = x

Switch sides

x = 729

Verify Solutions:

x = 729

True

The solution is

x = 729

lo g_{x} (\frac{1}{32}) = - \frac{5}{2}

x, lo g_{3 x - 4} (k) = 2

- lo g_{10} (x) = 12.603

1.4 = - lo g_{10} (x)

lo g_{10} (9 x - 1) = 2