Math Help Logs and Exps
So... I'm absolutely stuck on this problem.
http://oi60.tinypic.com/2mhdk5t.jpg
A similar one that I have the ''answer'' to is:
4log(base3)2 - log(base3)4+5
And the answer being log(base3)972 <--- Which I can't seem to understand why it's that. I must have copied it wrong.
Help, please?
June 10, 2014
2 Comments • Newest first
[quote=klu180]For your example problem 4log(base3)2 - log(base3)4+5
4log(base3)2 = log(base3)2^4 = log(base3)16
5 = log(base3)3^5 =log(base3)243
Based on the law of logs
log(baseb)M - log(baseb)N = log(baseb)M/N so
log(base3)16 - log(base3)4 = log(base3)16/4 = log(base3)4
likewise log(baseb)M + log(baseb)N = log(baseb)MN so
log(base3)4 + log(base3)243 = log(base3)4*243 = log(base3)972
Based on that I think you could figure out your question[/quote]
Haha, I just came to that conclusion right now. Thanks for the extra support. c:
For your example problem 4log(base3)2 - log(base3)4+5
4log(base3)2 = log(base3)2^4 = log(base3)16 (<-- Another law of logs, log(baseb)M^N = Nlog(baseb)M)
5 = log(base3)3^5 =log(base3)243 (When dealing with logs, turn the number into a log, I think you know about basic log expressions)
Based on the law of logs
log(baseb)M - log(baseb)N = log(baseb)M/N so
log(base3)16 - log(base3)4 = log(base3)16/4 = log(base3)4
likewise log(baseb)M + log(baseb)N = log(baseb)MN so
log(base3)4 + log(base3)243 = log(base3)4*243 = log(base3)972
Based on that I think you could figure out your question