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

The answer to log_{y}(125)=3 is y=5

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log_{y}(125)=3

lo g_{y} (125) = 3

y = 5

Solution steps

lo g_{y} (125) = 3

Apply log rules

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

Multiply both sides by

lo g_{125} (y)

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

Simplify

1 = 3 lo g_{125} (y)

Switch sides

3 lo g_{125} (y) = 1

Divide both sides by

3

lo g_{125} (y) = \frac{1}{3}

Apply log rules

y = 5

Verify Solutions:

y = 5

True

The solution is

y = 5

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

2 lo g_{3} (- x + 1) = 6

lo g_{10} (x + 1) = lo g_{10} (1 - x)

lo g_{10} (x) (81) = 4

3 ln (6 x) = - 3