What is the answer to log_{x}(125)=-3/2 ?

The answer to log_{x}(125)=-3/2 is x= 1/25

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log_{x}(125)=-3/2

lo g_{x} (125) = - \frac{3}{2}

x = \frac{1}{25}

Decimal Notation

x = 0.04

Solution steps

lo g_{x} (125) = - \frac{3}{2}

Apply log rules

\frac{1}{lo g _{125} ( x )} = - \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = - lo g_{125} (x) \cdot 3

Simplify

2 = - lo g_{125} (x) \cdot 3

Switch sides

- lo g_{125} (x) \cdot 3 = 2

Divide both sides by

- 3

lo g_{125} (x) = - \frac{2}{3}

Apply log rules

x = \frac{1}{25}

Verify Solutions:

x = \frac{1}{25}

True

The solution is

x = \frac{1}{25}

\frac{- 1}{3} = lo g_{27} (x)

4 lo g_{2} (\frac{3}{m}) = 8

2 lo g_{3} (x) = lo g_{3} (18 - x)

ln (1 + 6 y - 2 y^{2}) = 0

ln (11.7 - 2.5 x) = x - 4

What is the answer to log_{x}(125)=-3/2 ?
The answer to log_{x}(125)=-3/2 is x= 1/25
Solve for x: log_{x}(125)=-3/2
The solution is x= 1/25