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anonymous
 5 years ago
Hi, me again. Can anybody help me solve [ 5^(x4) = 6^(2x+1) ] with natural logarithms?
anonymous
 5 years ago
Hi, me again. Can anybody help me solve [ 5^(x4) = 6^(2x+1) ] with natural logarithms?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Take logarithms on both sides of equality: It will be \[(x4)\log5=(2x+1)\log6 \implies x=\frac{\log6+4\log5}{\log52\log6}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Aweome! Thanks so much for your help tonight; my teacher's given us very sparse information on the topic and none of the practice questions have answers with working. Thanks again!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm, just to make sure, exactly how did you rearrange it to get that final fraction?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Multiply x with log5 and then 4 with log5. Its just the distributive property. \[(x4)\log5=x\log54\log5 \ and\ (2x+1)\log6=2x\log6+\log6\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then equate the two sides collecting the x terms and the constant terms. Its easy right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, like indices! Yep, thanks saubhik! :)
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