Logx+log(x-3)=1

Question

Logx+log(x-3)=1

anonymous · Answer

sum of log is same as log of product

jim_thompson5910 · Answer

$$\large \log(x)+\log(x-3)=1$$



$$\large \log(x(x-3))=1$$



$$\large x(x-3)=10^1$$



$$\large x(x-3)=10$$



$$\large x^2-3x=10$$



$$\large x^2-3x-10=0$$



$$\large (x-5)(x+2)=0$$



$$\large x-5=0 \ \ \textrm{or} \ \ x+2=0$$



$$\large x=5 \ \ \textrm{or} \ \ x=-2$$



Since you cannot take the log of a negative number, this means that the only answer is x = 5

anonymous · Answer

meaning rewrite 
$$\log(a)+\log(b)=\log(ab)$$ then rewrite in equivalent exponential form

anonymous · Answer

@jimthompson you are fast at that latex wow!

anonymous · Answer

in your face math

anonymous · Answer

$$\log(x^{2}-3x)=1$$
$$10^{1}=x^{2}-3x$$
$$x^{2}-3x-10=0$$
(x-5)(x+2)=0
x=5or x=-2

please confirm

liizzyliizz · Answer

:D Thanks so much, You guys have saved me, and have refreshed my memory for AP Calc.

anonymous · Answer

the more familiar you are with logs and exponentials the happier you will be in calc, believe me

liizzyliizz · Answer

I did fairly well with Logs and exponential.. The summer has ruined that for me though. But how do you about graphing in calc;  that is my concern for this year...