A community for students.
Here's the question you clicked on:
 0 viewing
3psilon
 3 years ago
3^x = 5^y what is x/y ? Plz help . I'm terrible with Logs
3psilon
 3 years ago
3^x = 5^y what is x/y ? Plz help . I'm terrible with Logs

This Question is Closed

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Bah, logs with different bases . . . Gimme a sec to remember how to do this.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Ok, got it. Take \(\large log_3\) of both sides.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Then you can use the logarithm power rule.

3psilon
 3 years ago
Best ResponseYou've already chosen the best response.0Do you mind working please? @CliffSedge . I'm a little rusty on the rules

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Oh, I suppose so. It's pretty easy.. Given \(\large 3^x = 5^y\) \(\large log_3\) both sides \(\large log_3(3^x) = log_3(5^y)\) \(\large x = 3^x = log_3(5^y)\) Understand so far?

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2*oops, never mind that = "3x" in the last line. I thought I deleted that.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Should be \(\large x=log_3(5^y)\)

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Do you see that \(\large log_3(3^x)=x\) ?

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2The logarithm function tells you what the exponent is on that base.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2So, since a logarithm is an exponent, and if you have a powertoapower, you multiply exponents, \(\large log_3(5^y)=y log_3(5)\) . I think you can get the rest from here.

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1351900584391:dw Still having some trouble pimp or you figured this one out already. Figured I'd throw my 2 cents just in case :D Sorry that it's a little bit messy, hopefully you can follow it. The asterisks are log rules.

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2I don't think the change of base is necessary, but it is good to know how to do such a thing.

3psilon
 3 years ago
Best ResponseYou've already chosen the best response.0I found this way to do itdw:1351900905598:dw

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0If we wants to be able to plug it into a calculator it is necessary :) Depends what type of answer his teacher wants I suppose! :D

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0wow that's tough to read :(

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2That is an equivalent way, sure. It uses the same log rules but in a different order.

3psilon
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry I just put them both to the 1/y

zepdrix
 3 years ago
Best ResponseYou've already chosen the best response.0took the y'th root? Oh that's clever ^^

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.2Makes sense since it's looking for a ratio of exponents, but also takes a leap of imagination that might be hard to see. The straightforward way is easier to remember and just as efficient.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.