Determine whether the statement below is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

Question

log_b (x³ + y³) = 3 log_b x + 3 log_by

 Utilize the sub/superscripts (x²/x₂), as well as, Insert Math Equations if needed. 

Answer 1

The log of two numbers being multiplied is the sum of their individual logs:

log(x•y) = log(x) + log(y)

But the log of two numbers being added cannot be simplified:

log(x + y) = log(x + y)

So in this case, the statement is FALSE. One way to correct it is replace the "+" on the left side with a "•" like this:

log_b(x³ • y³) = 3log_b(x) + 3log_b(y)