If two equivalent logarithmic expressions have the same base, then the arguments must be equal.
x=4
Practice makes perfect
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.
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.
The argument of a logarithmic function cannot be negative, so both log_4(-4) and log_4(-16) are undefined, and -16 is an extraneous solution. Let's now check for the x=4.
