SOLUTION: Please help! Final is on Monday. Here is the problem I am stuck on: (2/5)^x = 7^1-x I came up with ln7/ln(2/5)+ln7 = 1.890 but my roomate keeps coming up with something

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help! Final is on Monday. Here is the problem I am stuck on: (2/5)^x = 7^1-x I came up with ln7/ln(2/5)+ln7 = 1.890 but my roomate keeps coming up with something      Log On


   

Question 80792: Please help! Final is on Monday.
Here is the problem I am stuck on:
(2/5)^x = 7^1-x
I came up with ln7/ln(2/5)+ln7 = 1.890 but my roomate keeps coming up with something different. Am I right? Thank you so much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F5%29%5Ex+=+7%5E%281-x%29

log%28%282%2F5%29%5Ex%29+=+log%287%5E%281-x%29%29 Take the log base 10 of both sides(in this case, it doesn't matter which base we use)

xlog%282%2F5%29+=+%281-x%29log%287%29 Use the identity log%28x%5Ey%29=ylog%28x%29

xlog%282%2F5%29+=+log%287%29-xlog%287%29 Distribute log(7) to (1-x)

xlog%282%2F5%29%2Bxlog%287%29+=+log%287%29 Get all x terms to one side

x%28log%282%2F5%29%2Blog%287%29%29+=+log%287%29 Factor out an x

x+=+log%287%29%2F%28log%282%2F5%29%2Blog%287%29%29 Divide both sides by log%282%2F5%29%2Blog%287%29 to isolate x

So you are correct the answer is

x+=+log%287%29%2F%28log%282%2F5%29%2Blog%287%29%29 or x=1.88993148010236


Check:
Plug in x=1.88993148010236 to check
%282%2F5%29%5E1.88993148010236+=+7%5E%281-1.88993148010236%29

0.1769785572734+=+7%5E%28-0.88993148010236%29
0.1769785572734+=+0.1769785572734 works