Exercise 58 Page 533

To evaluate the given logarithm, we will start by writing a logarithmic equation. log_2 1/32=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 2 must be raised to get 132. log_2 1/32= x ⇔ 1/32= 2^x Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.

1/32 = 2^x

WritePow

Write as a power

1/2^5 = 2^x

FracToNegExponent

1/a^m=a^(- m)

2^(-5) = 2^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.

2^(-5) = 2^x

EquateExponents

Equate exponents

-5 = x

RearrangeEqn

Rearrange equation

x = -5