Question

Give the domain on which the equation is defined. In particular, describe the set of x for which the equation is defined, using interval notation.
Solve for the unknown variable. Show all your work.
e^(x-5)*e^(3x+8)=19

Answer 1

law's of exponents

e^(x-5)*e^(3x+8) = 19
e^(x-5+3x+8) = 19
e^(4x+3) = 19

take the natural log, which is base "e" of both sides.

ln[e^(4x+3)] = ln[19]
4x +3 = ln[19]
4x = ln[19] - 3
x = (ln[19] - 3) / 4
x = -0.0139