1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ahat [919]
3 years ago
12

For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

.
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

You might be interested in
1/2+1/4= <br><br> 3/4+1/4=<br><br> What is the difference
son4ous [18]
1/2 + 1/4 = 3/4
3/4 + 1/4 = 1
4 0
3 years ago
Read 2 more answers
Importance of sports​
Softa [21]

Answer:

Sports is beneficial to physical health and well-being

as well as for growth and development, it decreases chances of contracting diseases and illnesses such as cardiovascular disease, lowers fat - intake as well as improves memory and relieves stress.

3 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE HELP
bekas [8.4K]

Answer:

its the last choice

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The Eastons traveled 190 miles on a trip to Grandma’s house. At the end of the trip the odometer read 7,602 miles. Write and sol
Black_prince [1.1K]

Answer:

X+190=7602

X=7412

Step-by-step explanation:

The odometer read 7412 miles at the beginning of the trip.

3 0
3 years ago
Can you help me out with this one?
shepuryov [24]

Answer: 98

Step-by-step explanation:

98 / (-7) = -14

7 0
3 years ago
Read 2 more answers
Other questions:
  • Point P is chosen at random in a circle. If a square is inscribed in the circle, what is the probability that P lies outside the
    8·1 answer
  • the sum of present ages ofa father and his son is 60years .if both of them live until the son becomes as old as the father is no
    15·1 answer
  • A convex hexagon has interior angles with measures x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100), what is the v
    13·1 answer
  • Q. What is the GCF of 18k and 15k3<br> answer choices<br> АЗk2<br> В Зk3<br> СЗk<br> D5k
    5·1 answer
  • hank cut a cake into 12 equal pieces and ate 2 pieces. he has 10/12 of the cake left to serve on plates. what part of the cake d
    7·2 answers
  • The points (2, 1), (3, 3), (4, 5), and (5, 6) are collinear. True or False
    14·2 answers
  • In the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),
    6·1 answer
  • What does the equation √3/8
    5·1 answer
  • Which of these numbers: 3,4,18,111,123,340,345,456,555 are divisible by 3 but not 9
    6·1 answer
  • Which expression is equivalent to 12b + 3a? choices: a (a + b) x 12 b 3 (4b + a) c ab x 12 x 3 d (12 x 3) + (b x a)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!