SOLUTION: log6 (3) + log5 (2) is equivalent to A 0 B ln(2) * ln (6) C 1 / ln(6) D ln(2) / ln (9) E 9 F [ln(5)*ln(3)) + ln(2)*ln(6))]/ [ln(5)*ln(6)] I have no idea where to start

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log6 (3) + log5 (2) is equivalent to A 0 B ln(2) * ln (6) C 1 / ln(6) D ln(2) / ln (9) E 9 F [ln(5)*ln(3)) + ln(2)*ln(6))]/ [ln(5)*ln(6)] I have no idea where to start       Log On


   

Question 124444: log6 (3) + log5 (2) is equivalent to
A 0
B ln(2) * ln (6)
C 1 / ln(6)
D ln(2) / ln (9)
E 9
F [ln(5)*ln(3)) + ln(2)*ln(6))]/ [ln(5)*ln(6)]
I have no idea where to start with this one.
If someone could show me the steps to come to the correct answer it would be very much appriciated. Thank you very much for your time!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log6 (3) + log5 (2)

There is a formula that allows you to convert logs of different base numbers to ln, which is log base e.

log%28b%2CM%29=+%28ln+M%29%2F%28ln+b%29+

log+%286%2C3%29%2B+log%285%2C2%29
%28ln+3%29%2F%28ln+6%29+%2B+%28ln2%29%2F%28ln5%29+

Next, find a common denominator:
+%28%28ln+3%29%28ln5%29+%2B+%28ln+2%29%28ln+6%29%29%2F%28%28ln+6%29%2Aln%285%29%29+

This looks like the last choice F.

For additional explanation of logarithms, please see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Go to the "MATH IN LIVING COLOR" pages, choose "College Algebra", and look at topics in Chapter 4 LOGARITHMS.

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