Question

Having some trouble with exponential problems...

Ok, so say you have e ^(2x)=e ^(x+1). How would you go about solving for x?

Alternatively, if you had 4^(-x)=2^(x+1) how would you find THAT x?

Any help to either or both of those problems would be extremely useful :)

Answer 1

e ^(2x)=e ^(x+1)
you have same base e, so just equate the exponents:
2x = x+1
then solve for x

Answer 2

whenever you have an equation of that form try to make the base of the exponent the same or one. For exampleNow you can directly equate the exponents of both sides; \[-2x=x+1\]