1296^2n=216^n+10

Question

1296^2n=216^n+10

anonymous · Answer

can you first give the prime factorization for 1296 and 216 for me?

anonymous · Answer

do you need help?

anonymous · Answer

nevermind! sorry! but can you help with this one? $$6^{6n}\le1/1296$$

anonymous · Answer

yes... notice that 1296 came up again.... i'm going to ask you the same thing... give me the prime facorization of 1296

anonymous · Answer

i am very bad at math! what do you mean by prime factorization?

anonymous · Answer

in order to solve your problem we need to write 1296 as some power of 6.  having the prime factorization greatly helps...

anonymous · Answer

can you write 1296 as a power of 6?

anonymous · Answer

i don't think you can do this problem by elementary methods. where does it come from?  this is very hard to solve

anonymous · Answer

or asnswer this:  6^x = 1296 , what's x?

anonymous · Answer

n would be four. i am doing classes online and this came up. my answer choices are $$n \le -24, n \le -2/3, n \le -2/3, or n \le -5/6$$

anonymous · Answer

i can tell you the answer but that's not the procedure here.  i am willing to help you get the answer though if you'd put in the time...

anonymous · Answer

well i have 35 minutes, and i still need help on another problem. please make my life a little easier

mertsj · Answer

$$6^{6n }\le\frac{1}{1296}$$
$$6^{6n}\le6^{-4}$$
$$6n \le-4$$
$$n \le\frac{-2}{3}$$

anonymous · Answer

thanks guys but i forgot to say this test is timed! it just ran out ): i appreciate it though!

mertsj · Answer

Are you sure you posted the very first problem right?  Is the +10 the right number?