Natural Logs

[elcatracho]

Hey I had a question about these two problems.. the one problem is
e^(2x)-6e^(x)+5=0 the way I thought you could do that was to take natrual log of the two and make it.... 2xLne-xln6e+ln5= 0 but than i got stuck because i don't know if that was legal.

My second question was 3ln2x-3=12 for this one i wondered if I could put the 3 as an exponent but I wasn't sure if that would have been helpful or not. Can you please help me?

 

[stapel]

(No instructions were included within your post. Are you supposed to be solving? If so, then treat the first equation as a quadratic in e^x:

. . . . .(e^x)² - 6(e^x) + 5 = 0

. . . . .(e^x - 5)(e^x - 1) = 0

...and solve the two linear factors. (No, your "taking logs of each individual term separately" is not at all "legal". Sorry.)

For the second equation, assuming you're solving, isolate the log (assuming the "x" is inside the log, along with the "2"), and then raise both sides as powers on e.

Eliz.