Hi Heather;
log_{3} (3x6) = log_{3} (2x+1)
Before I answer this, I was like to briefly review logarithms.
Let's just say that...
log_{3} (3x6) = 5
I randomly selected the number 5.
This would resolve as...
3x6=3^{5}
Do you see how the base _{3} moved to the other side of the = sign and became a 3, whereas the 5 rose to exponential status of
^{5}?
I love the way Megan described the components as base, exponent and "answer". If she does not mind, I intend to use it in future answers.
In the equation you provided, the base of _{3} appears on both sides of the equation. Henceforth...
log_{3} (3x6) = log_{3} (2x+1)
we can cancel these.
3x6=2x+1
Let's add 6 to both sides as we proceed to isolate x...
3x6+6=2x+1+6
3x=2x+7
Let's subtract 2x from both sides...
2x+3x=2x+72x
x=7
Let's verify...
(3x6) ??? (2x+1)
[3(7)6] ??? [2(7)+1]
216 ??? 14+1
15=15
All Good!
11/1/2013

Vivian L.