
exponents and powers
i got this question in my exam today
find x if 16^{3x}=32^{5x13}
i keep getting it as 65/17 which i know is wrong.i really want to find my mistake before the papers are out.
a friend of mine got the answer as 8 but he's not sure either.please help.(Crying)
thanks in advance

Re: exponents and powers
You are both incorrect. We are given:
$\displaystyle 16^{3x}=32^{5x13}$
Since both bases are powers of 2, we may write:
$\displaystyle (2^4)^{3x}=(2^5)^{5x13}$
$\displaystyle 2^{12x}=2^{25x65}$
Now, equate the exponents, and solve for $\displaystyle x$.

Re: exponents and powers
yes i did get that part.
then since the base is common,
12x=25x65
65=25x12x
65=17x
x=65/17
hmmmm is there anything wrong with this? cuz actually i wasn't present when this topic was being taught.

Re: exponents and powers

Re: exponents and powers
How could I be so stupid?!
Why does It always happen to me.?!!

Re: exponents and powers

Re: exponents and powers
Yes, that is the correct solution.
As for not making simple mistakes, I will let you know if I ever stop making them! :)

Re: exponents and powers
Ah............no one is perfect.