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pottersheep
Group Title
Please help! Show that each statement is true (LOGS)
[1/log base 5 of a] + [1/log base 3 of a] = [1/logbase 15a]
 one year ago
 one year ago
pottersheep Group Title
Please help! Show that each statement is true (LOGS) [1/log base 5 of a] + [1/log base 3 of a] = [1/logbase 15a]
 one year ago
 one year ago

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pottersheep Group TitleBest ResponseYou've already chosen the best response.0
sorry last one is log base 15 of a
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
lets add on the left
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{\log_3(a)+\log_5(a)}{\log_3(a)\times \log_5(a)}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
now lets flip it and see if we can show it is the same as \(\log_{15}(a)\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that is, can we show \[\frac{\log_3(a)\times \log_5(a)}{\log_3(a)+\log_5(a)}=\log_15(a)\] and i think we can do it using the change of base formula and writing everything in terms of \(\log_{15}(x)\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
do you know the change of base formula?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you get a nasty compound fraction on the left, i will see if i can write it \[\frac{\frac{\log_{15}(a)}{\log_{15}(5)}\times \frac{\log_{15}(a)}{\log_{15}(5)}}{\frac{\log_{15}(a)}{\log_{15}(5)}+\frac{\log_{15}(a)}{\log_{15}(3)}}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
to clear the compound fraction, multiply top and bottom by \(\log_{15}(3)\log_{15}(5)\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the numerator will be \[\log_{15}(a)\times \log_{15}(a)\] and the denominator will be \[\log_{15}(a)\log_{15}(5)+\log_{15}(a)+\log_{15}(5)\] factor as \[\log_{15}(a)\left(\log_{15}(5)+\log_{15}(3)\right)\] which gives \[\log_{15}(a)\times \log_{15}(3\times 5)=\log_{15}(a)\times 1\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
typo above, second line should be \[\log_{15}(a)\log_{15}(5)+\log_{15}(a)\log_{15}(5)\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
cancel and you get what you want
 one year ago

pottersheep Group TitleBest ResponseYou've already chosen the best response.0
oooooo Thanks!
 one year ago
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