math:solving for an exponent.
posted by Sar on .
I can't get the right answer, where am I going wrong?
7.0x10^9= (6.7x10^9)(2.72^r*3)
1.04 = 2.72^r*3
When I solve for this, I get ln (1.40) = 0.03922 then 0.03922 / 3 = 0.0130
So my r equals 0.0130
BUT the teacher says the answer is
0.05 = r *3
0.02 = r
What did I do wrong? I am so confused!! Help please. Show steps

is that 2.72^{3r} ?
then 1.0447=2.72^3r
Ln 1.0447=3r *ln 2.72
r= 1/3 (ln1.0447/ln2.72)= 0.0148574093
When you are dealing with logs, you need to keep as many digits as you can. You are correct. 
1.04 = 2.7^(3r)
ln 1.04 = 3r ln 2.72
but that still does not give .05 = 3r
Typo in problem? 
No. The math he did was handwritten. I guess he must have made a mistake because this is driving me nuts. Everything listed in my post is CORRECTLY copied from the piece of paper I got it on.

Bob, thank you. I thought I was going insane there for a minute. I guess the professor made a mistake. We are all human (but it drives me crazy when I'm trying to study haha)