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

AI Thread Summary
The equation 2^(5x) = 3^x(5^(x+3)) is being solved using logarithms. The user attempted to apply natural logarithms but struggled to isolate x. They received a hint to use the property of logarithms that states log(ab) = log(a) + log(b). After some guidance, the user expressed confidence in their understanding of the solution process. The discussion emphasizes the importance of logarithmic properties in solving exponential equations.
0range
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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!
 
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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...

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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!
 

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