SOLUTION: Please help me solve this equation: {{{ log base 3(7x) = log base 3(2x+.05) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve this equation: {{{ log base 3(7x) = log base 3(2x+.05) }}}      Log On


   

Question 262881: Please help me solve this equation: +log+base+3%287x%29+=+log+base+3%282x%2B.05%29+
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C7x%29+=+log%283%2C2x+%2B+.05%29
I can use the general rule
if
(1) log%28a%2Cb%29+=+log%28a%2Cc%29
then
(2) b+=+c
To show this, rewrite (1) as
y+=+log%28a%2Cb%29
y+=+log%28a%2Cc%29
then
a%5Ey+=+b
a%5Ey+=+c
so, b+=+c
therefore
7x+=+2x+%2B+.05
5x+=+.05
x+=+.01
check answer:
log%283%2C7x%29+=+log%283%2C2x+%2B+.05%29
log%283%2C7%2A.01%29+=+log%283%2C2%2A.01+%2B+.05%29
log%283%2C.07%29+=+log%283%2C.07%29
OK