Solve for t a 4ln2t510 b 12 5e3t 8Solutiona 4ln2t 510 ln

Solve for t:

a.) 4ln(2t+5)=10

b.) 12 - 5e^3t = 8

a) 4ln(2t + 5)=10

==> ln(2t + 5) = 10/4

==> ln(2t + 5) = 5/2 (since ln a = b ==> a = e^b)

==> 2t + 5 = e^5/2

==> 2t = e^5/2 - 5

==> t = (e^5/2 - 5)/2

==> t = 3.59125

b) 12 - 5e^3t = 8

==> 5e^3t = 12 - 8

==> 5e^3t = 4

==> e^3t = 4/5

Apply natural logarithm on both sides

==> ln e^3t = ln(4/5)

==> 3t (ln e) = ln(4/5) since ln a^b = b lna

==> 3t(1) = ln(4/5) since ln e = 1

==> 3t = ln(4/5)

==> t = (1/3) ln(4/5)

==> t = -0.0744