SOLUTION: Solve for x. log base 6 of (3x+14) - log base 6 of 5 = log base 6 of (2x) (I have gotten it down to log base 6 of (3x+14)- log base 6 of (2x)

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Question 598011: Solve for x.
log base 6 of (3x+14) - log base 6 of 5 = log base 6 of (2x)

(I have gotten it down to log base 6 of (3x+14)- log base 6 of (2x) - log base 6 of 5 = 0 and I know that you need to divide the logs next, but the 3 logs are tripping me up and I cannot figure out how to simplify it correctly.)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Solve for x.
log base 6 of (3x+14) - log base 6 of 5 = log base 6 of (2x)
log6(3x+14)-log6(5)=log6(2x)
log6(3x+14)-log6(5)-log6(2x)=0
log6(3x+14)-(log6(5)+log6(2x))=0
place under single log
log6[(3x+14)/(5*2x)]=0
log6[(3x+14)/(10x)]=0
convert to exponential form: base(6) raised to log of number(0)=number(3x+14)/(10x)
6^0=(3x+14)/(10x)=1
10x=3x+14
7x=14
x=2

SOLUTION: Solve for x. log base 6 of (3x+14) - log base 6 of 5 = log base 6 of (2x) (I have gotten it down to log base 6 of (3x+14)- log base 6 of (2x) - log base 6 of 5 = 0 and I kn