SOLUTION: HELP! im not sure how to go about solving these 2 simple problems! 1) ln(5x) + ln(9) = ln(6x + 2) 2) 3^(2x +4)= 27^ (x-7) i really dont just want the answers, i want to un

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: HELP! im not sure how to go about solving these 2 simple problems! 1) ln(5x) + ln(9) = ln(6x + 2) 2) 3^(2x +4)= 27^ (x-7) i really dont just want the answers, i want to un      Log On


   

Question 152548: HELP! im not sure how to go about solving these 2 simple problems!
1) ln(5x) + ln(9) = ln(6x + 2)
2) 3^(2x +4)= 27^ (x-7)
i really dont just want the answers, i want to understand how to do them, and why they work that way. if someone can please help me to understand this, i'd be very greatful. THANKS
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. Remember your log rule,
ln%28A%29%2Bln%28B%29=ln%28AB%29
Then
ln%285x%29%2Bln%289%29=ln%286x%2B2%29
ln%2845x%29=ln%286x%2B2%29
45x=6x%2B2
39x=2
x=2%2F39
.
.
.
2. Remember the exponentitation rule,
%28x%5EM%29%5EN=x%5E%28M%2AN%29
Then
3%5E%282x%2B4%29=27%5E%28x-7%29
3%5E%282x%2B4%29=%283%5E3%29%5E%28x-7%29
3%5E%282x%2B4%29=3%5E%283%2A%28x-7%29%29
2x%2B4=3%2A%28x-7%29
2x%2B4=3x-21
-x=-25
x=25