<PRE><B>Question 135077</B>
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. 
:
{{{(1/4)^x = 5^(1-x)}}}
:
Find the log of both sides
{{{log((1/4)^x) = log(5^(1-x))}}}
Use the log equivalent of exponents:
{{{x*log(1/4) = (1-x)*log(5)}}}
Find the logs:
-.60206x = .69897(1-x)
:
-.60206x = .69897 - .69897x
:
+.69897x - .60206x = .69897
:
.09691x = .69897
x = {{{.69897/.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?

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