What is the answer to log_{x}(5)=2 ?

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

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log_{x}(5)=2

lo g_{x} (5) = 2

x = 5

Decimal Notation

x = 2.23606 \dots

Solution steps

lo g_{x} (5) = 2

Apply log rules

\frac{1}{lo g _{5} ( x )} = 2

Multiply both sides by

lo g_{5} (x)

\frac{1}{lo g _{5} ( x )} lo g_{5} (x) = 2 lo g_{5} (x)

Simplify

1 = 2 lo g_{5} (x)

Switch sides

2 lo g_{5} (x) = 1

Divide both sides by

2

lo g_{5} (x) = \frac{1}{2}

Apply log rules

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{5} (x - 6) = 1 - lo g_{5} (x - 2)

lo g_{6} (x) + lo g_{6} (x - 9) = 2

ln (x) = 2.5

e^{l n (x^{2})} + x = 6

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