What is the answer to log_{a}(25)=2 ?

The answer to log_{a}(25)=2 is a=5

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log_{a}(25)=2

lo g_{a} (25) = 2

a = 5

Solution steps

lo g_{a} (25) = 2

Apply log rules

\frac{1}{lo g _{25} ( a )} = 2

Multiply both sides by

lo g_{25} (a)

\frac{1}{lo g _{25} ( a )} lo g_{25} (a) = 2 lo g_{25} (a)

Simplify

1 = 2 lo g_{25} (a)

Switch sides

2 lo g_{25} (a) = 1

Divide both sides by

2

lo g_{25} (a) = \frac{1}{2}

Apply log rules

a = 5

Verify Solutions:

a = 5

True

The solution is

a = 5

2 ln (x + 3) = ln (x + 1) + 3 ln (2)

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

lo g_{7} (5 x - 6) = 3

lo g_{5} (2 x - 23) = lo g_{5} (x + 51)

ln (1 - x) = 0