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
Ymorist [56]
3 years ago
15

Can someone explain the process getting from:

Mathematics
1 answer:
spin [16.1K]3 years ago
6 0
\rm 5=e^{3b}

The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.

We'll take log of each side.
Log of what base tho?

Well, the base of our exponential is e,
so we'll take log base e of each side.

\rm log_e(5)=log_e(e^{3b})

We'll apply one of our log rules next:
\rm \log(x^y)=y\cdot\log(x)

This allows us to take the exponent out of the log,

\rm log_e(5)=(3b)log_e(e)

Another thing to remember about logs:
When the base of the log matches the inside of the log,
then the whole thing is simply 1,
\rm log_{10}(10)=1
\rm log_5(5)=1
\rm log_e(e)=1

So our equation simplifies to this,

\rm log_e(5)=(3b)\cdot1

As a final step, divide both sides by 3,

\rm \frac13log_e(5)=b

k, hope that helps!


You might be interested in
How do you Calculate the volume of each cylinder
DiKsa [7]

Volume= π·R²·H

π is Pi, approximately 3.142

R is the radius of the circular end of the cylinder

H is height of the cylinder

8 0
3 years ago
Read 2 more answers
Drag statements and reasons to each row to show why the slope of the line between P and Q is the same as the slope between Q and
Delvig [45]

hi i know i’m late but to help out any future people, the answer is

Row One: Statement: 3/2=slope Reason: Definition of Slope

Row 2: Statement: 3/2=6/4 Reason: Triangle A is similar to Triangle B

5 0
3 years ago
Read 2 more answers
Eleven oz of ground coffee is 2 cups. How many cups is 12 oz?​
SVETLANKA909090 [29]

Answer:

66 oz

Step-by-step explanation:

Every 2 cups have 11 ounces of ground coffee. Two times six is 12, so 11 times 6 is 66.

Another explanation is-

2/12 = 11/x

12 times 11 is 132. Then divide that by two to get 66

4 0
3 years ago
Please help and thanks in advance <br><br><br> Add 0.65 and 0.24. How many tenths are in the sum?
elena-s [515]
There are 8 tenths in the sum. .65+.24 is .89. tenths are the first digit to the right of the decimal. 80 and 8x10=80
6 0
3 years ago
Which number does Not represent 4.701
konstantin123 [22]

Answer:

4.702 does not represent 4.701

Step-by-step explanation:

#teamtrees #WAP (Water And Plant)

6 0
2 years ago
Read 2 more answers
Other questions:
  • Draw a graph of this linear inequality y&lt;2
    9·1 answer
  • HELP ASAP What are some real world examples you can think of that involve using the coordinate plane? Feel free to use the inter
    7·1 answer
  • This symbol ≥ means that one number is ____ ____ or equal to another number.
    13·2 answers
  • Weight gain during pregnancy. In 2004, the state of North Carolina released to the public a large data set containing informatio
    14·1 answer
  • Someone help me please
    6·1 answer
  • Please help me solve this.
    13·1 answer
  • (I'd like the quick and short answer please a long explaination is unnecessary)
    14·1 answer
  • Triangles A B C, D E F, G H I, and J K L are shown. Angles A C B, D F E, H I G, and K L J are right angles. The length of side A
    5·2 answers
  • 2. Which statement is not true in the equation
    12·1 answer
  • Evaluate the following functions.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!