Exercise 59 Page 533

To evaluate the given logarithm, we will start by writing a logarithmic equation. log_5 5sqrt(5)=x In order to solve this equation, we can rewrite it as an exponential equation by using the definition of a logarithm. log_b x= y ⇔ x= b^y The above means that the logarithm y is the exponent to which b must be raised to get x. For our exercise, x is the exponent to which 5 must be raised to get 5sqrt(5). log_5 5sqrt(5)= x ⇔ 5sqrt(5)= 5^x Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.

5sqrt(5)=5^x

SqrtToPowD

sqrt(a)=a^(12)

5* 5^(12) = 5^x

MultBasePow

a*a^m=a^(1+m)

5^(1+ 12) = 5^x

Now we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal.

5^(1+ 12) = 5^x

EquateExponents

Equate exponents

1+1/2 = x

OneToFrac

Rewrite 1 as 2/2

2/2+1/2 = x

AddFrac

Add fractions

3/2 = x

RearrangeEqn

Rearrange equation

x = 3/2