What is the answer to log_{x}(2)= 1/5 ?

The answer to log_{x}(2)= 1/5 is x=32

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log_{x}(2)= 1/5

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

x = 32

Solution steps

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

Apply log rules

\frac{1}{lo g _{2} ( x )} = \frac{1}{5}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 5 = lo g_{2} (x) \cdot 1

Simplify

5 = lo g_{2} (x)

Apply log rules

32 = x

Switch sides

x = 32

Verify Solutions:

x = 32

True

The solution is

x = 32

lo g_{10} (x) = - 4.52

- 9 lo g_{2} (5 r - 2) = - 9

lo g_{10} (x) = - 4.41

lo g_{10} (x) = - 14.6745

lo g_{x} (2) - 3 lo g_{2} (x) = 2