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+--- Thread: More Math Help (/showthread.php?tid=17577)
More Math Help - loveapples - 11-28-2010
So I'm doing logs??in math class, and am stuck on 3 questions. >_>
1. ln 45 + ln (x-4) = ln (5x-4)
2. log (x^2 - 49) - 1 = log (x + 7)
3. log'3'(13-x) - log'3'(x+3) = 1
(That's Log base 3 (13-x) minus Log base 3 (x+3) equals to 1)
RE: More Math Help - Namine - 11-28-2010
1. Combine the sum of ln first so:
ln [45(x-4)] = ln (5x-4)
Put everything as powers of e, so you have
e^[ln 45(x-4)] = e^[ln (5x-4)]
That'll cancel out all the ln, so you are only left with
45(x-4) = 5x-4
Just solve for x then.
2. Expand the difference of square first, so:
log [ (x+7)(x-7)] - 1 = log (x+7)
Break up the multiplication inside the log there:
log (x+7) + log (x-7) - 1 = log (x+7)
log (x-7) = 1
Since log10 = 1, x-7 must also equal to 10, so x is 17.
3. Change to base 10 (or use ln, but i hate ln) so it's easier to deal with first.
log(13-x)/log3 - log(x+3)/log3 = 1
log(13-x) - log(x+3) = log3
Again change the difference of log, combining into division for the number inside log.
log[(13-x)/(x+3)] = log3
Since both side are the same, compare the number inside the log function.
(13-x)/(x+3) = 3
And now you can solve for x.
RE: More Math Help - Zaratus - 11-28-2010
1. ln 45 + ln (x-4) = ln (45* (x-4)), then just e^() and you have a linear equation.
2. log (x^2-49) - 1 = log (x^2-49) - log(10) = log ( (x^2-49)/10), then just 10^() and you have a quadratic equation. .. That you can solve with binomic formula like Nami there. Or do quadratic formula and get two solutions where one isn't defined for log(x+7).
Lemme think a sec about 3rd.
3. log'3'(13-x) - log'3'(x+3) = 1
(That's Log base 3 (13-x) minus Log base 3 (x+3) equals to 1)
log'3'(13-x) - log'3'(x+3) = log'3'( (13-x)/(x+3) then 3^() and linear equation again.
RE: More Math Help - loveapples - 11-29-2010
Thanks again for the help! I appreciate it.
RE: More Math Help - mahawirasd - 11-30-2010
wow, 2nd year of high-school seems so far away from me now... i feel old...
-w-
RE: More Math Help - Spuznik - 12-10-2010
O.O I think my class did this today... but I was asleep for most of it, it scared me when I woke up, now I have to try to figure out what it was we were doing. :D