SOLUTION: I'm doomed...I don't understand this...please help. Solve the equation. Write answers in exact form using logarithms if needed (no decimals): log3(x+24)-log3(x+2)=2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I'm doomed...I don't understand this...please help. Solve the equation. Write answers in exact form using logarithms if needed (no decimals): log3(x+24)-log3(x+2)=2      Log On


   

Question 769062: I'm doomed...I don't understand this...please help.
Solve the equation. Write answers in exact form using logarithms if needed (no decimals): log3(x+24)-log3(x+2)=2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
log3(x+24) - log3(x+2) = 2

Use the logarithm rule log%28b%2Cu%29-log%28b%2Cv%29=log%28b%2Cu%2Fv%29 on the left side:

log3%28%28x%2B24%29%2F%28x%2B2%29%29 = 2

Use the rule to change a log equation into an exponential equation:

                       log%28b%2Cu%29=v  becomes u=b%5Ev

%28x%2B24%29%2F%28x%2B2%29 = 32

%28x%2B24%29%2F%28x%2B2%29 = 9

Multiply through by (x + 2)

x + 24 = 9(x + 2)

x + 24 = 9x + 18

   -8x = -6

     x = %28-6%29%2F%28-8%29

     x = 3%2F4



Edwin