0.5t=ln(1.5t+20) solve for t

Question

0.5t=ln(1.5t+20)

 

 

Answer 1

to rid yourself of "ln", exponentiate (on base e).

therefore e^0.5 = 1.5t + 20

Now you can finish the job, easily, using a calculator.

Answer 2

If there is no typo in the problem statement, you will end up with a transcendental equation.

 

0.5t = ln(0.5t + 20)

 

Take e⁽⁾ of both sides.

 

e^0.5t = 0.5t + 20

 

An approximate solution may be obtained using numerical methods, such as Newton's iterative method, or a graphical method.  This does not look like a problem that you can solve exactly.