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

[EternityMech]

Hardest Math Problem EVAR!

Homework Statement

300 * 1,05^x = 160 * 1.07^x

Homework Equations

what is x?

The Attempt at a Solution

140 = 1,05^x / 1.07^x

i can solve this using a graphic calculator but i want to do it mathematically.

 

[Dick]

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!

 

[EternityMech]

is it 300/140 or 300/160?

thanks for the help.

 

[Dick]

is it 300/140 or 300/160?

thanks for the help.

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

 

[Cyosis]

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

 

[EternityMech]

(1.05/1.07)^x = 160 / 300

got it muchos gracias.