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

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Homework Help Overview

The discussion revolves around solving an equation involving exponential growth rates, specifically in the form of 300 * 1.05^x = 160 * 1.07^x. Participants are exploring methods to isolate the variable x mathematically.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss transforming the equation into a logarithmic form and question the correct ratio of constants involved in the equation. There is also a mention of using a graphical calculator versus a purely mathematical approach.

Discussion Status

Some guidance has been offered regarding the use of logarithms to simplify the equation, and there is an ongoing clarification about the correct values to use in the equation. Multiple interpretations of the constants are being explored, indicating a productive discussion.

Contextual Notes

There appears to be confusion regarding the constants in the equation, with participants questioning whether to use 300/140 or 300/160. This uncertainty may affect the direction of the discussion.

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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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