How do you solve log_3(x+16) - log_3(x) = log_3(2)?

2 Answers
Jun 7, 2016

x=16

Explanation:

First, note that they are all in log_3, so we simplify the left-hand side to get

log_3((x+16)/x) = log_3 2
=> (x+16)/x = 2, 2x=x+16, x=16

Jun 7, 2016

16=x

Explanation:

The log laws suggest that when to log's with the same base subtract from one another, it can be written as

log_a(x)-log_a(y)=log_a(x/y)

Therefore, our equation can be simplified into

log_3((x+16)/x)=log_3(2)

Therefore (x+16)/x=2

x+16=2x

16=x