Exercise 60 Page 533

To evaluate the given logarithm, we will start by writing a logarithmic equation. log_(16) 8=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 16 must be raised to get 8. log_(16) 8= x ⇔ 8= 16^x Finally, to solve the exponential equation, we will rewrite the terms so that they have a common base.

8 = 16^x

WritePow

Write as a power

2^3 = (2^4)^x

PowPow

(a^m)^n=a^(m* n)

2^3 = 2^(4x)

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

2^3 = 2^(4x)

EquateExponents

Equate exponents

3 = 4x

DivEqn

.LHS /4.=.RHS /4.

3/4 = x

RearrangeEqn

Rearrange equation

x = 3/4