What is the answer to log_{a}(25)=4 ?

The answer to log_{a}(25)=4 is a=sqrt(5)

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log_{a}(25)=4

lo g_{a} (25) = 4

a = 5

Decimal Notation

a = 2.23606 \dots

Solution steps

lo g_{a} (25) = 4

Apply log rules

\frac{1}{lo g _{25} ( a )} = 4

Multiply both sides by

lo g_{25} (a)

\frac{1}{lo g _{25} ( a )} lo g_{25} (a) = 4 lo g_{25} (a)

Simplify

1 = 4 lo g_{25} (a)

Switch sides

4 lo g_{25} (a) = 1

Divide both sides by

4

lo g_{25} (a) = \frac{1}{4}

Apply log rules

a = 5

Verify Solutions:

a = 5

True

The solution is

a = 5

4 - lo g_{10} (x^{2} - x + 4) = 3

ln (\frac{( x - 2 )}{8}) = 2

2 lo g_{10} (x + 5) + lo g_{3} (9) = 2

3 lo g_{4} (6 x) = 9

5 ln (x) = - 15