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

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pottersheep
 2 years ago
Best ResponseYou've already chosen the best response.0sorry last one is log base 15 of a

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1lets add on the left

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\log_3(a)+\log_5(a)}{\log_3(a)\times \log_5(a)}\]

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1that 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 \(\log_{15}(x)\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1do you know the change of base formula?

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

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the 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 \[\log_{15}(a)\times \log_{15}(3\times 5)=\log_{15}(a)\times 1\]

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1cancel and you get what you want
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