How do you solve the equation 2 log4(x + 7)-log4(16) = 2?

1 Answer
Aug 11, 2016

x= 9

Explanation:

When working with a log equation, the term must be all logs or all numbers.
Change the RHS to a log term as well.

color(red)(2)log_4 (x+7) - log_4 16 = log_4 16 " "2 = log_4 16

log_4 (x+7)^color(red)(2) - log_4 16 = log_4 16

"If logs are being subtracted, the numbers are being divided"

log_4 ((x+7)^2/16)= log_4 16

(x+7)^2/16 = 16" if log A = log B, A = B"

(x+7)^2 = 256" cross multiply"

x+7 = 16" only pos root is valid"

x= 9