SOLUTION: I'm working on a summer math review packet for school, and came across a logarithm problem that I can't seem to get correct: {{{ log( 3, 12 )-2log( 3, 2 ) }}} The answer sheet s

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm working on a summer math review packet for school, and came across a logarithm problem that I can't seem to get correct: {{{ log( 3, 12 )-2log( 3, 2 ) }}} The answer sheet s      Log On


   

Question 328860: I'm working on a summer math review packet for school, and came across a logarithm problem that I can't seem to get correct: +log%28+3%2C+12+%29-2log%28+3%2C+2+%29+
The answer sheet says the answer is 1, but I keep getting 2. Could you help me figure this out? Thanks!
Found 2 solutions by galactus, solver91311:
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
Try the change of base thing.
ln%2812%29%2Fln%283%29-2%2Aln%282%29%2Fln%283%29
%28ln%2812%29-2%2Aln%282%29%29%2Fln%283%29
%28ln%2812%29-ln%284%29%29%2Fln%283%29
ln%2812%2F4%29%2Fln%283%29
ln%283%29%2Fln%283%29=1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Your answer sheet is correct.



First use:



to write



Then use the fact that the difference of the logs is the log of the quotient:



to write:

.

Then use the definition of the logarithm function



To write:



Then use the fact that



to write



John