3 to the 2x power+ 3 to the X+1 power - 4=0?

Answer 1

Make the substitution z = 3^x. The equation becomes

z^2 + 3*z - 4 = 0

This can be factored:

(z + 4)*(z - 1) = 0

z = -4, z = 1

3^x = -4, 3^x = 1 for the second of these, x = 0. The other root is imaginary: take log of both sides
x*log(3) = log(-4), x = log(-4)/log(3) = [log(4) + log(-1)]/log(3)= log(4)/log(3) + log(-1)/log(3)

Using natural logs, log(4) = 1.386, log(3) = 1.099, and since e^πi = -1, log(-1) = πi, so the other root is
1.262 + (π/3)i