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

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) (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.
:

:
Find the log of both sides

Use the log equivalent of exponents:

Find the logs:
-.60206x = .69897(1-x)
:
-.60206x = .69897 - .69897x
:
+.69897x - .60206x = .69897
:
.09691x = .69897
x =
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?

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