Hi,

I would really appreciate some help with a few questions. Please explain or show me the best way to solve problems in the attached files. Sorry for so many questions in one post

Thx!

hey jman I'm not sure if these are the best/quickest ways but they worked out well for me.

1) manipulate left side -
2^x - 2^x/2^2
2^x ( 1 - 1/4 )
2^x (3/4)
(2^x/4)3
3 ( 2^x/2^2)
(2^x-2)3

now that both sides are identical put together powers in equation x - 2 = 13, so x = 15

2) Create equation where: Pp = purchasing price, Ps = selling price

Ps = Pp + 40/100Ps

sub in Pp = 150

Ps = 150 + 40/100Ps (1 linear equation with 1 unknown)

Ps = 250

3) - express second term as 1/(2^2)^18 = 1/2^36 = 1/(2*2^35)

so now we have: 1/(5^m) * 1/(2*2^35) = 1/(2*10^35)

recognize rule that (eg) 1/(5^2) * 1/(2^2) = 1/(10^2)

Therefore if 1/2 * 1/(5^m) * 1/(2^35) = 1/2 * 1/(10^35) then m = 35

Thanks very much, that is very helpful.