Exercise 7 Page 336

We want to solve an equation involving more than one logarithm. To do so, we will use the Product Property of Logarithms. log_b mn = log_b m + log_b n First, we will isolate the logarithm that contains the variable. Then, we can use the above property to isolate the variable from the logarithm. Recall that if the base is not stated, it is 10. Next, we will use the fact that if two equivalent logarithmic expressions have the same base, then the arguments must be equal. log_b x=log_b y ⇔ x= y Let's apply the above property to our equation and then solve for x by factoring. To check for extraneous solutions, we will substitute both 5 and -4 for x in the given equation one at a time. Since substituting 5 for x in the given equation produces a true statement, x=5 is the solution to our equation. Let's now check x=-4. The argument of a logarithmic function cannot be negative, so both log(-20) and log(-5) are undefined, and -4 is an extraneous solution.