Wednesday

April 16, 2014

April 16, 2014

Posted by **Claudia** on Friday, July 26, 2013 at 10:26pm.

2.solve 4(3^2x)=e^x

- math -
**Reiny**, Friday, July 26, 2013 at 10:56pm1. 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/(1-2ln3) or appr. -1.1579

check:

LS = 4(3^-2.3158... = .31413784

RS = e^-1.157923.. = .31413784 , how about that?

**Related Questions**

Shayna - Find the value of a so that the function f(x) = xe^(ax) has critical ...

Calculus - Find the derivatives, dy/dx for the following functions. a. x^2y^4 = ...

L'Hopital's rule - Find lim x->1+ of [(1/(x-1))-(1/lnx)]. Here is my work...

calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...

Calculus 1 - Find the derivative of y with respect to x. y=(x^6/6)(lnx)-(x^6/36...

Math - Find the coordinates of the turning point and determine wether it is ...

calculus - USE INTEGRATION BY PARTS TO FIND EACH INTEGRAL ƪx lnx dx

calculus - (a) find the intervals on which f is incrs or decrs. (b) find the ...

Calculus - F(x) = 1-x and g(x) = 1/x Write in the form (ax + b)/(cx + d) a.What ...

math - I can't figure out this problem: AX+BY=C SOLVE FOR Y AX+BY=C SOLVE FOR Y ...