SOLUTION: Solve by using logarithms, or otherwise, the equations: i) {{{(2)^(x+1)+(2)^(x)=9}}} ii) {{{(2)^(x-2)(3)^(x+2)=(6)^(x)}}} *PLEASE ANSWER AS SOON AS POSSIBLE BRO =)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve by using logarithms, or otherwise, the equations: i) {{{(2)^(x+1)+(2)^(x)=9}}} ii) {{{(2)^(x-2)(3)^(x+2)=(6)^(x)}}} *PLEASE ANSWER AS SOON AS POSSIBLE BRO =)      Log On


   

Question 466703: Solve by using logarithms, or otherwise, the equations:
i) %282%29%5E%28x%2B1%29%2B%282%29%5E%28x%29=9
ii) %282%29%5E%28x-2%29%283%29%5E%28x%2B2%29=%286%29%5E%28x%29
*PLEASE ANSWER AS SOON AS POSSIBLE BRO =)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
i) %282%29%5E%28x%2B1%29%2B%282%29%5E%28x%29=9
2%5Ex%282%5E1+%2B+2%5E0%29+=+9
2%5Ex%2A3+=+9
2%5Ex+=+3
x*log(2) = log(3)
x = log(3)/log(2)
x =~ 1.58496
----------------
ii) %282%29%5E%28x-2%29%283%29%5E%28x%2B2%29=%286%29%5E%28x%29
(x-2)log(2) + (x+2)log(3) = x*log(6)
xlog(2) - log(4) + xlog(3) + log(9) = xlog(6)
x(log(2) + log(3) - log(6)) = log(4/9)
x*log(1) = log(4/9)
0 = log(4/9) --> no solution