log base 3 ^X + log base of 3^(x+1)=log base of 3 ^2 +log base3(x+3)
2006-12-06 13:48:31 · 11 answers · asked by katie 4 in Science & Mathematics ➔ Mathematics
41
2006-12-06 14:04:45 · answer #1 · answered by Anonymous · 0⤊ 1⤋
I'm going to rewrite this, for easier reading.
log[base3](x) + log[base3]((x+1)) = log[base3](2) + log[base3](x+3)
Your first step is to remember the log property that
log(a) + log(b) = log(a+b). We combine logs into a single log like so:
log[base3](x(x+1)) = log[base3](2 * (x+3))
Now, we can take the antilog of both sides, to get rid of the logs.
x(x+1) = 2(x+3)
x^2 + x = 2x + 6
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0, therefore x = 3 and x = -2
HOWEVER, you can't assume those values work. You have to plug them into the original equation, and IF you end up taking the log of a negative number, you discard that solution. There's already a problem with x = -2, since
log[base3](x), the first term of your equation, is already invalid, so you throw away the -2.
x = 3 has no problems though. Therefore, the only solution is
x = 3.
2006-12-06 13:58:26 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
log base 3 ^X + log base of 3^(x+1)=log base of 3 ^2 +log base3(x+3)
log base3^x(x+1)=log base3^ 2(x+3)
thus, x(x+1)=2(x+3) since both sides have log base 3, can remove
therefore, x^2+x=2x+6
X^2-X-6=0
thus (x-3)(x+2)=0
hence x=3 or x=-2(undefined)
For logarithms to be defined, x=3
2006-12-06 13:57:05 · answer #3 · answered by mr warlords 2 · 0⤊ 0⤋
log base 3 ^X + log base of 3^(x+1)=log base of 3 ^2 +log base3(x+3)
log base 3^x log base 3^(x+1) = Log base 9 + log base 3(x+3)
It is difficult to understand what you are asking.
It seems that you are not telling what to take the log of in each instance. I read your question as follows:
(log with base 3^x) (log with base 3 ^(x+1))= log with base 9 +
log with base 3(x+3).
The problem is that you have not said what we are .taking the logarithm of.
Suppose we are taking the logarithm of Z. Then,
(log _3^x (Z)(log_3^(x+1) (Z)=log_9 (Z) + log _3(x+3)(Z)
So (log_3^x (Z))( log_5^(x+1) (Z)= log_9 (Z) +log_3(x+3) (Z)
IOt would appear that your question is improperly stated
2006-12-06 14:44:31 · answer #4 · answered by ironduke8159 7 · 0⤊ 1⤋
a million. The seat in an automoble would not flow, the automobile that's in does. 2. the guy interior the mask is the catcher on a baseball group and the guy on 0.33 is afraid to flow to residing house plate.
2016-10-04 23:47:50 · answer #5 · answered by dunkelberger 4 · 0⤊ 0⤋
I bet ya can't rub your belly and pat your head at the same time. You just shorted out my calculator...thanks a lot.
2006-12-06 13:56:14 · answer #6 · answered by steve 5 · 0⤊ 2⤋
whoa imma need 100 points to solve that
2006-12-06 13:50:51 · answer #7 · answered by Anonymous · 0⤊ 2⤋
i'll just give u a calculator, so you can do ur homework
2006-12-06 13:55:28 · answer #8 · answered by jamaica 5 · 0⤊ 1⤋
SORRY I WANT MORE THEN TEN POINTS 2 DO THAT
2006-12-06 13:50:32 · answer #9 · answered by Anonymous · 0⤊ 1⤋
I don't want to do your homework
2006-12-06 13:50:05 · answer #10 · answered by Anonymous · 0⤊ 3⤋