25^x = (√5) ÷ (125^x)
2007-01-17 11:50:50 · 3 answers · asked by ItalianStallion 2 in Science & Mathematics ➔ Mathematics
(5^2)^x=5^(1/2) / (5^3)^x
5^(2x)=5^(1/2) / 5^(3x)
5^(2x)=5^(1/2 - 3x)
2x=1/2 - 3x
5x=1/2
x=1/10
2007-01-17 11:56:17 · answer #1 · answered by Professor Maddie 4 · 3⤊ 0⤋
25^x*125^x = sqrt5 so (25*125)^x=sqrt5
x* log(25*125)= log(sqrt5)====> x= log(sqrt5)/log(25*125)logsqrt5 = log(5)/2 log (25*125) = log (5^5) = 5 log5
so x =1/10
2007-01-17 20:03:37 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
take the log of both sides...
xlog(25) = log(â5/125^x)
xlog(25) = log(â5) - xlog125
x(log(25)+log(125)) = log(â5)
xlog(3125) = log(â5)
x = log(â5)/log(3125)...final answer
lol, this equals 1/10 either way will work, but mine was a little harder
2007-01-17 20:01:18 · answer #3 · answered by J J 3 · 0⤊ 0⤋