Evaluate log base square root of 13 of 20

Rewrite as an equation.

log13(20)=x

Rewrite log13(20)=x in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then logb(x)=y is equivalent to by=x.

13x=20

Create equivalent expressions in the equation that all have equal bases.

13x=132.33589974

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

x=2.33589974

The variable x is equal to 2.33589974.

2.33589974