Solving for X: A Challenging Math Problem with Exponential Growth Rates

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AI Thread Summary
The discussion revolves around solving the equation 300 * 1.05^x = 160 * 1.07^x for the variable x. A user suggests transforming the equation into a logarithmic form to simplify the problem, emphasizing the use of logarithmic properties to create a linear equation. There is a clarification regarding the correct ratio to use, with the consensus settling on 300/160. The conversation highlights the importance of mathematical manipulation and the application of logarithmic laws in solving exponential equations. Overall, the focus is on finding a mathematical solution rather than relying on graphical methods.
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Hardest Math Problem EVAR!

Homework Statement



300 * 1,05x = 160 * 1.07x

Homework Equations



what is x?


The Attempt at a Solution



140 = 1,05x / 1.07x

i can solve this using a graphic calculator but i want to do it mathematically.
 
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Your combined form should be 300/140=1.07^x/1.05^x. Take the log (any base) of both sides. Do you see how the laws of logarithms log(a*b)=log(a)+lob(b) and log(a^x)=x*log(a) can make this the easiest linear equation EVAR!
 
Last edited:


is it 300/140 or 300/160?

thanks for the help.
 


EternityMech said:
is it 300/140 or 300/160?

thanks for the help.

300/160, of course. Sorry about the slip.
 


Edit: I mistook your post for being the solution to the problem
 


(1.05/1.07)x = 160 / 300

got it muchos gracias.
 

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