Solve 2^(5x)=3^x(5^(x+3)) Logarithm Exercise

Click For Summary

Homework Help Overview

The problem involves solving the equation 2^(5x) = 3^x(5^(x+3)), which falls under the subject area of logarithms and exponential equations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation using logarithms but encounters difficulty isolating x. Some participants suggest using properties of logarithms, specifically the product rule.

Discussion Status

Participants are engaged in exploring different approaches to the problem. A hint regarding the use of logarithmic properties has been provided, and the original poster expresses gratitude for the guidance received.

Contextual Notes

The original poster mentions challenges with LaTeX formatting and seeks clarification on etiquette regarding its use in the forum.

0range
Messages
11
Reaction score
0

Homework Statement



2^{5x}=3^x(5^{x+3})

Homework Equations


The Attempt at a Solution



ln2^{5x}=ln3^x(ln5^{x+3})

5xln2=xln3(x+3)ln5

Here's where I get stuck... I've tried a bunch of different manipulation, but can't seem to isolate x...

Thanks in advance!
 
Physics news on Phys.org
Hint: Remember that log (ab) = log (a) + log (b) Check the RHS of your equation
 
Thanks for the direction! I think I've got it...

5v23wg.jpg


It's late and I still suck at LaTeX, is it okay to do this, or is it against etiquette?

Thanks again for your help!
 
Welcome to PF, Orange! :smile:

0range said:
Thanks for the direction! I think I've got it...

It's late and I still suck at LaTeX, is it okay to do this, or is it against etiquette?

Thanks again for your help!

It is okay to do that, and you did get it.

Cheers!
 
Thanks!
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
Replies
1
Views
2K
Replies
7
Views
2K
Replies
3
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K