math
posted by Claudia on .
1.Express (xe^x)^2=30e^(x) in the form lnx=ax+b,and find the value of a and of b .
2.solve 4(3^2x)=e^x

1. take ln of both sides
ln(x e^x)^2 = ln(30 e^x)
2 lnx + 2ln e^x = ln30 + ln e^x
2lnx + 2x = ln30 x
2 lnx = 3x + ln30
lnx = (3/2)x + (1/2)ln30 or (3/2)x + ln (√30)
comparing this with ax + b
a = 3/2 , b = ln √30
2. take ln of both sides and use rules of logs
ln (4(3^2x) ) = ln e^x
ln4 + xln3 = x
x  2xln3 = ln4
x(1  2ln3) = ln4
x = ln4/(12ln3) or appr. 1.1579
check:
LS = 4(3^2.3158... = .31413784
RS = e^1.157923.. = .31413784 , how about that?