Question

Solve the equation. First, express your answer in terms of natural logarithms (for instance, x = (2 + ln(5)) / (ln(3)).

28e^-x/3=54.5

x=

Now use a calculator to find an approximation for your answer. (Round your answer to two decimal places.)

x =

Answer 1

divide both sides by 28 then take ln to each side.

Answer 2

-x/3 = ln (54.5/28)
-x = 3ln(54.5/28)=ln{(54.5/28)}^3

Answer 3

what about the e?

Answer 4

multiply both sides by -1 and use the fact that -1lna = ln(a^-1)

Answer 5

ln e = 1

Answer 6

ln(e^-x/3)=(-x/3)lne=-x/3

Answer 7

why dont we divide by -1?

Answer 8

mutliply or divide both sides by -1 to solve for x

Answer 9

so whats the final answer?

Answer 10

x = ln(28^3) - ln (54.5^3)

Answer 11

or x = 3ln28 - 3ln54.5

Answer 12

what about the second answer?

Answer 13

they are both the same answer since ln(28^3) = 3ln28 and ln(54.5^3) = 3ln54.5

Answer 14

i meant the answer for part 2 of the question

Answer 15

type 3ln28 - 3ln54.5 into your calculator

Answer 16

i dont see ln on my calc

Answer 17

nevermind. thanks for all the help!