What is the answer to the following problems? (a) 1/4=2^x (b) 125=25^3/5^x?

(a)
1/4 = 2^x
2^x = 4^(-1)
2^x = 2^(-2)
x = -2


====
(b)
125 = 25^3/5^x
125 (5^x) = 25^3
5^3 (5^x) = (5^2)^3
5^x = 5^6 / 5^3
5^x = 5^3
x = 3

a)
x = - 2

b)
Presentation is dodgy !
so have to take a GUESS at :-
125 = [ 25^3 / [ 5^x ]
5^{3 + x ] = 5^6
3 + x = 6
x = 3
PS
Use brackets !!!!

(a)
x = (ln(1/4) + 2*i*pi*n) / ln(2), for any integer n
x = -2 + ((2*i*pi*n)/ln(2)), for any integer n
x =~ -2 + 9.0647202836543876192553658914333*i*n, for any integer n
If x is a real number, then n = 0, so x = -2
http://www.wolframalpha.com/input/?i=1%2F4%3D2^x

(b)
125 = (25^3) / (5^x)
125 = 15625 / (5^x)
125 * (5^x) = 15625
5^x = 15625/125
5^x = 125
x = (ln(125) + 2*i*pi*n) / ln(5), for any integer n
x = 3 + ((2*i*pi*n)/ln(5)), for any integer n
x =~ 3 + 3.9039625316623427965473047644973*i*n, for any integer n
If x is a real number, then n = 0, so x = 3
http://www.wolframalpha.com/input/?i=125%3D25^3%2F5^x

a)
2^x = 1/4
x log(2) = log(1/4)
x = log(1/4) / log(2)
x = -log(4)/log(2)
x = -log(2^2) / log(2)
x = -2 log(2)/log(2)
x = -2

b)
125 = 25^3 / 5^x
divide both sides by 25^3
125/ 25^3 = 1/ 5^x
125/ (25*25*25) = 1/ 5^x

1/125 = 1/ 5^x
5^x = 125
x log(5) = log(125)
x = log(125) /log(5)
x = log(5^3) / log(5)
x = 3 log(5) /log(5)
x = 3

(a)
2^x = 1/4 = 1/2^2 = 2 ^(-2)
So x = -2

(b)
125 = 25^3 / 5^x
So 5^x = 25^3 / 125 = (5^2)^3 / 5^3 = 5^6 / 5^3 = 5^3
So x = 3