# exponents and powers

• Oct 3rd 2012, 03:59 AM
NormalKid
exponents and powers
i got this question in my exam today

find x if 163x=325x-13

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)

• Oct 3rd 2012, 04:07 AM
MarkFL
Re: exponents and powers
You are both incorrect. We are given:

$16^{3x}=32^{5x-13}$

Since both bases are powers of 2, we may write:

$(2^4)^{3x}=(2^5)^{5x-13}$

$2^{12x}=2^{25x-65}$

Now, equate the exponents, and solve for $x$.
• Oct 3rd 2012, 10:18 AM
NormalKid
Re: exponents and powers
yes i did get that part.
then since the base is common,
12x=25x-65
65=25x-12x
65=17x
x=65/17

hmmmm is there anything wrong with this? cuz actually i wasn't present when this topic was being taught.
• Oct 3rd 2012, 10:22 AM
MarkFL
Re: exponents and powers
25-12=13
• Oct 3rd 2012, 09:07 PM
NormalKid
Re: exponents and powers
How could I be so stupid?!
Why does It always happen to me.?!!
• Oct 3rd 2012, 09:13 PM
NormalKid
Re: exponents and powers
yes it is
• Oct 3rd 2012, 09:13 PM
MarkFL
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! :)
• Oct 3rd 2012, 09:14 PM
NormalKid
Re: exponents and powers
Ah............no one is perfect.