Can I further simplify (Log 9) / (Log 3)?

2009-04-25 3:24 pm
How can I further simplify (Log 9) / (Log 3)? When I put the numbers in a calculator it tells me that it is 2, but I'm not supposed to use a calculator. Is it because 3^2 = 9 that I got 2 or is this just a coincidence and I should have left my simplified answer as (log 9) / (log 3)?

回答 (7)

2009-04-25 3:36 pm
✔ 最佳答案
(Log 9) / (Log 3) = log (3^2)/ log 3 = 2 log3/log3 = 2
2016-10-04 9:18 am
________________________________________... log_3 (80 one) + log_3 (6^a million/5)^-8 - log_3 (one hundred forty four/512) - log_3 (4)^a million/5 + log_3 (a million/3)^4/3 ??????????????????????????????????????... EDIT here is yet differently to try this ??????????????????????????????????????... technique 2 log?80 one + log?((6¹??)??) - log?(one hundred forty four/512) - log?(4¹??) + log?((?)??³) = log?(3?) + log?(6??????) - log?(9/32) - log?((2²)¹??) + log?((3?¹)??³) = 4·log?(3) + log?(3??????2??????) - log?(3²/2?) - log?(2²??) + log?(3???³) = 4 + log?(3??????) + log?(2??????) - [log?(3²) - log?(2?)] - (²??)·log?(2) - (???)log?(3) = 4 - (???)·log?(3) - (???)·log?(2) - [2·log?(3) - 5·log?(2)] - (²??)·log?(2) - (???)log?(3) = 4 - (???) - (???)·log?(2) - [2 - 5·log?(2)] - (²??)·log?(2) - (???) = 4 - (???) - (???)·log?(2) - 2 + 5·log?(2) - (²??)·log?(2) - (???) = 4 - (???) - 2 - (???) - (???)·log?(2) + 5·log?(2) - (²??)·log?(2) = ?? ?? - (14/15) ???? + ???????? (-??? + 5 - ²??)·log?(2) = ?? ?? - (14/15) ???? + ???????? ??????? 3·log?(2) = ?? ?? - (14/15) ???? + ???????? ??????? ?log?(2³) = - (14/15) + log?(8) ? 0.95945592 ?????????? ? answer ??????????????????????????????????????... technique a million ?????????? ?? 80 one·(6¹??)??·(?)??³ = log? —————————— ?????????? ??? (one hundred forty four/512)·4¹?? ?????????? ?? 80 one·(6????)·3???³ = log? —————————— ?????????? ??? ? (9/32)·4¹?? ????????? ?? ??????? 32·80 one = log? —————————— ?????????? ?? 9·4¹??·(6???)·3??³ ????????? ?? ??????? 32·9 = log? —————————— ?????????? ? word that each little thing ?????????? ?? 4¹??·(2???·3???)·3??³ ?????????? ????? would properly be written as powers of two or 3 ????????? ?? ????? ? 2?·3² = log? —————————— ?????????? (2²)¹??·2???·3???·3??³ ????????? ?? ????? 2?·3² = log? ————————– ?????????? 2²??·2???·3???·3??³ ????????? ?? ????? 2?·3² = log? ————————– ?????????? ?? 2¹???·3???¹? ????????? ?? ????? 2?·3² = log? ————————– ?????????? ?? ? 2²·3???¹? = log?(2??²·3²?????¹??) = log?(2³·3?¹??¹?) = log?(2³) + log?(3?¹??¹?) = log?(2³) - (14/15)·log?3 = log?(8) - (14/15) ?????????? ? answer ???? log(8) = ———— ? (14/15) ?????????? ? answer ???? log(3) ? 0.95945592 ?????????? ? answer ___________________________
2009-04-25 5:06 pm
log(9)/log(3)
= log(3^2)/log(3)
= 2log(3)/log(3)
= 2/1
= 2
2009-04-25 3:34 pm
it is simple
log9=log3 pr 2
=2log3
then
2log3/log3
cancel out log3
it will be 2/1=2
2009-04-25 3:33 pm
log9 = log3² = 2log3 (properties of logarithms)

2log3/log3 = 2 (log3 cancels)
2009-04-25 3:32 pm
=2log3/log3=2
2009-04-25 3:28 pm
log 9 = log 3^2 = 2log 3
then
(Log 9) / (Log 3)=2


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