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
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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:
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) (Show Source): You can put this solution on YOUR website!
Try the change of base thing.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your answer sheet is correct.
\ -\ 2\log_3(2))
First use:
\ =\ n\log_b(x))
to write
\ -\ 2\log_3(2)\ =\ \log_3(12)\ -\ \log_3(2^2)\ =\ \log_3(12)\ -\ \log_3(4))
Then use the fact that the difference of the logs is the log of the quotient:
 - \log_b(y) = log_b\left(\frac{x}{y}\right))
to write:
\ -\ \log_3(4)\ =\ \log_3(\frac{12}{4})\ =\ \log_3(3))
.
Then use the definition of the logarithm function
 \ \ \Rightarrow\ \ b^y = x)
To write:
\ \ \Rightarrow\ \ 3^y\ =\ 3)
Then use the fact that
to write
John
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