SOLUTION: Please help been stuck on this prob and can not solve. Express answer as decimal rounded to 3 decimal places. (1/4)x=5(1-x) x is exponent for 1/4 and 1-x is exponent for the

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help been stuck on this prob and can not solve. Express answer as decimal rounded to 3 decimal places. (1/4)x=5(1-x) x is exponent for 1/4 and 1-x is exponent for the       Log On


   

Question 135077: Please help been stuck on this prob and can not solve. Express answer as decimal rounded to 3 decimal places. (1/4)x=5(1-x) x is exponent for 1/4 and 1-x is exponent for the 5. Please help!!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Express answer as decimal rounded to 3 decimal places. (1/4)x=5(1-x) x is exponent for 1/4 and 1-x is exponent for the 5.
:
%281%2F4%29%5Ex+=+5%5E%281-x%29
:
Find the log of both sides
log%28%281%2F4%29%5Ex%29+=+log%285%5E%281-x%29%29
Use the log equivalent of exponents:
x%2Alog%281%2F4%29+=+%281-x%29%2Alog%285%29
Find the logs:
-.60206x = .69897(1-x)
:
-.60206x = .69897 - .69897x
:
+.69897x - .60206x = .69897
:
.09691x = .69897
x = .69897%2F.09691
x = 7.212568 Rounded to 7.213
:
:
Check on your calc:
enter .25^7.213 = 4.543(10^-5)
and
5^-.6.213 = 4.543(10^-5) close enough to confirm our solution
;
Did this make sense to you?