Solve for x

Question

1. 2^3x+1=3^x-2

 

Answer 1

Take the log of both sides of your equation.

Then log 1.2^(3x+1) = (3x+1)(.0792) = .2375x + .0792 and

log 3^(x-2) = (x-2)(.477) = .477x - .954.

So, .2375x + .0792 = .477x - .954

Solving for x gives x = 4.31

I hope this helps.

Answer 2

2^3x+1 = 3^x-2                                         take natural log of both sides

(3x+1) ln 2 = (x - 2) ln 3            distribute

3x ln 2 + ln 2 = x ln 3 - 2 ln 3      subtract x ln 3 from both sides

3x ln 2 - x ln 3 + ln 2 = - 2 ln 3   subtract ln 2 from both sides

3x ln 2 - x ln 3 = - ln 2 - 2 ln 3    factor out x

x(2 ln 2 - ln 3) = - ln 2 - 2 ln 3     divide both sides by (2 ln 2 - ln 3)

x = (- ln 2 - 2 ln 3) / (2 ln 2 - ln 3)