## 3psilon 3 years ago 3^x = 5^y what is x/y ? Plz help . I'm terrible with Logs

1. CliffSedge

Bah, logs with different bases . . . Gimme a sec to remember how to do this.

2. CliffSedge

Ok, got it. Take \(\large log_3\) of both sides.

3. CliffSedge

Then you can use the logarithm power rule.

4. 3psilon

Do you mind working please? @CliffSedge . I'm a little rusty on the rules

5. CliffSedge

Oh, 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?

6. CliffSedge

*oops, never mind that = "3x" in the last line. I thought I deleted that.

7. 3psilon

I'm sorta catching on

8. CliffSedge

Should be \(\large x=log_3(5^y)\)

9. CliffSedge

Do you see that \(\large log_3(3^x)=x\) ?

10. CliffSedge

The logarithm function tells you what the exponent is on that base.

11. CliffSedge

So, since a logarithm is an exponent, and if you have a power-to-a-power, you multiply exponents, \(\large log_3(5^y)=y log_3(5)\) . I think you can get the rest from here.

12. zepdrix

|dw: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.

13. CliffSedge

I don't think the change of base is necessary, but it is good to know how to do such a thing.

14. 3psilon

I found this way to do it|dw:1351900905598:dw|

15. zepdrix

If 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

16. zepdrix

wow that's tough to read :(

17. CliffSedge

That is an equivalent way, sure. It uses the same log rules but in a different order.

18. 3psilon

Sorry I just put them both to the 1/y

19. zepdrix

took the y'th root? Oh that's clever ^^

20. CliffSedge

Makes sense since it's looking for a ratio of exponents, but also takes a leap of imagination that might be hard to see. The straight-forward way is easier to remember and just as efficient.