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

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

(logx)^3 = 3 logx

Question

please help me find all exaclty solutions for these 2 equation:

9^x   + 14 =   3^(x+2)

(logx)^3   = 3 logx

anonymous · Answer

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

tkhunny · Answer

Is that $$9^{x+14}$$ or $$9^{x} + 14$$?

anonymous · Answer

the upper one

tkhunny · Answer

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.

anonymous · Answer

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

tkhunny · Answer

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?