What is the answer to log_{x}(100)=2 ?

The answer to log_{x}(100)=2 is x=10

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log_{x}(100)=2

lo g_{x} (100) = 2

x = 10

Solution steps

lo g_{x} (100) = 2

Apply log rules

\frac{1}{lo g _{100} ( x )} = 2

Multiply both sides by

lo g_{100} (x)

\frac{1}{lo g _{100} ( x )} lo g_{100} (x) = 2 lo g_{100} (x)

Simplify

1 = 2 lo g_{100} (x)

Switch sides

2 lo g_{100} (x) = 1

Divide both sides by

2

lo g_{100} (x) = \frac{1}{2}

Apply log rules

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

lo g_{x} (2) = \frac{1}{2}

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

lo g_{4} (x) = - \frac{3}{2}

lo g_{10} (3 x + 7) = 0

2 lo g_{10} (3 x - 7) = 8