Solve for t using natural logarithms. 6e^9t=8e^8t?

Question

if you can tell me exactly how to put it in the calculator, that would really help.

Answer 1

First, divide both sides by 2:

3e^(9t)=4e^(8t)

Take the ln of both sides:

ln[3e^(9t)]=ln[4e^(8t)]

Using rules of logarithms:

ln(3)+ln[e^(9t)]=ln4 + ln[e^(8t)]

Using definition of natural logarithms, this simplifies to

ln(3) +9t = ln(4) +8t

Subtract 8t from both sides:

ln(3)+t=ln(4)

Subtract ln(3) from both sides:

t=ln(4)-ln(3)

Use rules of logarithms:

t=ln(4/3)

Press 4

Press / ("divided by")

Press 3

Press =

press ln

You should get about .2877

_/

Answer 2

6e^9t-8e^8t=0

e^8t(6e^t-8)=0

e^8t=0 (not possible) or e^t=4/3

=>t=log[e](4/3)