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

The answer to log_{x}(5)= 1/5 is x=3125

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log_{x}(5)= 1/5

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

x = 3125

Solution steps

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

Apply log rules

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

Simplify

5 = lo g_{5} (x)

Apply log rules

3125 = x

Switch sides

x = 3125

Verify Solutions:

x = 3125

True

The solution is

x = 3125

lo g_{3} (x - 5) + lo g_{3} (x + 5) = 2

- 8 + lo g_{5} (x + 4) = - 6

x, ln (x^{2} + y^{2}) = 0

0.82 = ln (x)

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