How do you solve 2+log_3(2x+5)-log_3x=4?

1 Answer
Feb 8, 2015

I would start by collecting the logs on one side:

log_3(2x+5)-log_3(x)=4-2

I can use the fact that:
logM+logN=log(M/N)
Giving:

log_3((2x+5)/x)=2

Use the definition of logarithm:

log_ax=b ->a^b=x

Giving:

(2x+5)/x=3^2
2x+5=9x
7x=5
x=5/7

hope it helps