1. 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.

2. Re: exponents and powers

You are both incorrect. We are given:

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

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

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

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

Now, equate the exponents, and solve for $\displaystyle x$.

3. 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.

25-12=13

5. Re: exponents and powers

How could I be so stupid?!
Why does It always happen to me.?!!

yes it is

7. 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!

8. Re: exponents and powers

Ah............no one is perfect.