Exercise 57 Page 533

To evaluate the given logarithm, we will start by writing a logarithmic equation. log_4 64=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 4 must be raised to get 64. log_4 64= x ⇔ 64= 4^x Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.

64 =4^x

WritePow

Write as a power

4^3=4^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.

4^3=4^x

EquateExponents

Equate exponents

3 = x

RearrangeEqn

Rearrange equation

x=3