Exercise 19 Page 494

When bases are not the same, we can solve an exponential equation by taking the logarithm of each side of the equation. In our case, let 2 be the base of the logarithm. m=n ⇔ log_2 m = log_2 n Note that in order to take their logarithms, both m and n must be positive numbers. Let's now solve our equation.

4^(2x)=32

log_2(LHS)=log_2(RHS)

log_2 4^(2x)= log_2 32

log_2(a^m)= m* log_2(a)

2x log_2 4= log_2 32

WritePow

Write as a power

2x log_2 (2^2)= log_2 (2^5)

log_2(2^m)=m

2x(2)= 5

CommutativePropMult

Commutative Property of Multiplication

2(2)x= 5

Multiply

Multiply

4x=5

DivEqn

.LHS /4.=.RHS /4.

x=5/4