SOLUTION: log base 3 of (x+2)-log base 3 of (x-3)= log base 3 of 6 ; slove for x. i have a major test tommarrow and i'm lost on how to slove these! please and thank you for the help.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log base 3 of (x+2)-log base 3 of (x-3)= log base 3 of 6 ; slove for x. i have a major test tommarrow and i'm lost on how to slove these! please and thank you for the help.      Log On


   



Question 122347: log base 3 of (x+2)-log base 3 of (x-3)= log base 3 of 6 ; slove for x.
i have a major test tommarrow and i'm lost on how to slove these!
please and thank you for the help.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Your equation is:  log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29


First apply the difference of logs rule:
log%28b%2Ca%29-log%28b%2Cc%29=log%28b%2C%28a%2Fc%29%29


log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29
log%283%2C%28%28x%2B2%29%2F%28x-3%29%29%29=log%283%2C6%29


Now, if log%28b%2Ca%29=log%28b%2Cc%29 then a=c, so


log%283%2C%28%28x%2B2%29%2F%28x-3%29%29%29=log%283%2C6%29 => %28x%2B2%29%2F%28x-3%29=6


%28x%2B2%29%2F%28x-3%29=6
x%2B2=6%28x-3%29
x%2B2=6x-18
x-6x=-18-2
-5x=-20
x=4



Check the answer log%283%2C%28x%2B2%29%29-log%283%2C%28x-3%29%29=log%283%2C6%29 log%283%2C%284%2B2%29%29-log%283%2C%284-3%29%29=log%283%2C6%29 log%283%2C6%29-log%283%2C1%29=log%283%2C6%29 But log%28b%2C1%29=0, so log%283%2C6%29=log%283%2C6%29, Answer checks.