What is the answer to 2log_{x}(125)=6 ?

The answer to 2log_{x}(125)=6 is x=5

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2log_{x}(125)=6

2 lo g_{x} (125) = 6

x = 5

Solution steps

2 lo g_{x} (125) = 6

Divide both sides by

2

lo g_{x} (125) = 3

Apply log rules

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

Multiply both sides by

lo g_{125} (x)

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

Simplify

1 = 3 lo g_{125} (x)

Switch sides

3 lo g_{125} (x) = 1

Divide both sides by

3

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

Apply log rules

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

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

7 = 11.2 + lo g_{10} (x)

lo g_{3} (x^{3}) = lo g_{9} (27)

ln (x) = 9.976242681

1.02 = lo g_{10} (x)