Question

please help me find all exaclty solutions for these 2 equation:

9^x + 14 = 3^(x+2)

(logx)^3 = 3 logx

Answer 1

the first equation, do logs log both sides, see where that gets you

Answer 2

Is that \[9^{x+14}\] or \[9^{x} + 14\]?

Answer 3

the upper one

Answer 4

Well, that makes it possible. If it were the other, there woudl be no exact solution.

Observe that 9 = 3^2. This nearly completes the problem.

Answer 5

should i log both side? cuz if i do that, log 14 is a big mess

Answer 6

Did you use the hint?\[9^{x+14} = 3^{x+2}\] Using the hint, we have \[\left(3^{2}\right)^{x+14} = 3^{2x+28} = 3^{x+2}\] It is now pretty easy IF you see it. Do you?