Log equation...?

Question

ln 2x + ln 9x = ln 19

I really need instructions on how to do this. Thanks!!

the answer is x = (19/18)^1/2

Answer 1

There is a property of logs that says ln a + ln b = ln (ab)

So rewrite ln 2x + ln 9x as ln (2x*9x) = ln (18x^2)

You now have ln (18x^2) = ln (19) which means that since the logs are equal, so must be 18x^2 and 19.

18x^2 = 19

Divide both sides by 18, then
do both sides to the 1/2 power to cancel out the 2 exponent
and you'll have it.

Answer 2

ln 2x + ln 9x = ln 19
Ln addition implies multiplication in the original numbers and take the anti-log

(2x)(9x) = 19
18x^2 = 19
x^2 = 19/18

Therefore
x = (19/18)^1/2
.