here it is:x=10^y
subtract 10^y from both the sides
x-10^y=0
now subtract x from both the sides
-10^y = -x
divide by -1
-10^y/-1 = -x/-1
= 10^y = x
take log base 10 both sides
log10^y = logx
= ylog10=logx
y = logx/log10
The first part you go from x=10^y to -10^y=-x to 10^y=x. Is it not clear that if x=10^y then 10^y=x? The point is that any time A=B, then B=A.
Next, you have ended with y=log(x)/log(10). If the logarithms are base 10, what is log(10)? Can you use that to make your result simpler?
Next question: if t=log(u) (where the logarithm is base 10) then what does u equal?
i'am assuming this would end up in some number called 'e' which i came accross somewhere in the past.please help..i'am not sure what that number means and how to get it
The simple rules are these:
log(a.b) = log(a) + log(b)
hence
log(a^4) = log(a.a.a.a) = log(a)+log(a)+log(a)+log(a) = 4.log(a)
Therefore
if a = b^z
then log(a) = log(b^z)
so log(a) = z.log(b)
log_b(b) = 1 : Log (base b) of b is 1.
Hence log_b(b^2) = 2
log_b(b^3) = 3
and so on.
if x = b^y
then log_b(x) = log_b(b^y)
= y.log_b(b)
= y
If a = 10^b
then log(a) = log(10^b)
= b.log(10)
= b.1
= b
Finally, you need to study sections 1, 2 and 3 of this page:
http://en.wikipedia.org/wiki/Logarithm
What's on that page will also help you to understand the questions.