Hi, I was having some trouble with natural logarithms. Does anybody know how to solve [3^(2x)+4(3^(x+1)) = 189] for x using natural logarithms? I know it's a monster, sorry. :P

Question

anonymous · Answer

make substitution 3^x=y. It will be a quadratic.

anonymous · Answer

Sorry, but would you mind explaining that to me? So I write 3^(2X) + 4y = 189, and then what?

anonymous · Answer

No, the eqn will be y^2+4(3)y=189. Hope u can figure out why.:)

anonymous · Answer

Oh, I see! I think I can manage now. Thanks! :)

anonymous · Answer

4the second term is 12 multiplied by 3 to the x

anonymous · Answer

you let 3 raised to x be p, then you end up with a quadractic equation p squared plus tweleve p  equals 189

anonymous · Answer

p$$p ^{2}+12p=189$$