Solve the equation...

Question

Solve the equation 58e4t+1 = 30 exactly for t

Answer 1

Assuming 58e^(4t)+1=30

58e^(4t)+1=30

58e^(4t)=29

e^(4t)=29/58

e^(4t)=1/2

take the natural log of both sides

ln(e^[4t])=ln(1/2)

4t*ln(e)=ln(1/2)

ln(e)=1

4t*1=ln(1/2)

4t=ln(1/2)

t=ln(1/2)/4 or t=ln(0.5)/4 (exactly)

ln(1/2)=-0.69314718056

t=-0.69314718056/4

t=-0.17328679514 (approximately)