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

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

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

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

y = \frac{1}{25}

Solution steps

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

Apply log rules

\frac{1}{lo g _{125} ( y )} = - \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} (y) \cdot 3

Simplify

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

Switch sides

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

Divide both sides by

- 3

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

Apply log rules

y = \frac{1}{25}

Verify Solutions:

y = \frac{1}{25}

True

The solution is

y = \frac{1}{25}

lo g_{2} (x) + lo g_{x} (4) = 3

7 - 2 ln (x) = 2

H, p = - lo g_{10} (H)

10 lo g_{10} (x) = 3

10 lo g_{10} (x) = 1

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