need help with math?

Question

solve for x

1) ln(lnx)= 1

2) e^(ax) = Ce^(bx)

Answer 1

For

1) the inverse of ln is to take e^
use u substitution let ln(x) = u
now you have ln(u) = 1
take e to both sides (because if a=b then c^a=c^b)
e^ln(u)=e^1 so now you have
u = e^1
substitute back in ln(x) for u to get
ln(x) = e^1
**you should be able to take it from there**

the second one is harder but the first step is taking the natural log of both sides, then moving the c outside of the ln()
WITH MATH, there's a rule like ln(cx) = ln(c) + ln(x) I'm not sure what the rule is though, but apply it.

Answer 2

I will complete Doug's reply.

1) x=e^e, which is positive. Otherwise it wouldn't have been a root.

2) e^(ax) = Ce^(bx) take the log of both sides
ax=ln(C)+bx then do the algebra and get
x=ln(c)/(a-b)

First of all: C must be positive

Second: a must be different from b. Otherwise you would have got (a-b) x = ln C and (forall x) 0 = ln C which would have only made sense if and only if C would have been 1. For other values of C you wouldn't have had any x that would have been a root of this equation.

Ilusion

Answer 3

e^(ln(ln(x))) = e^1
ln(x) = e
e^(ln(x)) = e^e
x=e^e

e^(ax) = Ce^(bx) take the log of both sides
ax=ln(C)+bx then do the algebra and get
x=ln(c)/(a-b)

HTH

Doug