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-BARSIC- [3]
3 years ago
14

Applying Inverse Properties In Exercise,apply the inverse properties of logarithmic and exponential functions to simplify the ex

pression.See example 2.
In e2x - 1
Mathematics
1 answer:
kodGreya [7K]3 years ago
5 0

Answer:

The simplified form of the given expression is (2x-1).

Step-by-step explanation:

Consider the given expression is

\ln e^{2x-1}

According to the Inverse Properties of In

\ln e^x=x

In the given expression the power of e is (2x-1).

Using the Inverse Properties of In, we get

2x-1

Therefore, the simplified form of the given expression is (2x-1).

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Question 31 pts Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To
Sladkaya [172]

Answer:

P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Step-by-step explanation:

Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3

Basis: P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:

2(k+1) - 1 = 2k + 2 - 1

≤ 2 + k! (by the inductive hypothesis)

= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.

4 0
3 years ago
0.000309 in scientific notation
trasher [3.6K]
Hey there :)

Writing in scientific notation means a should be
0 ≤ a < 10

Therefore, 0.000309 will be written as
3.09 x 10ⁿ

3 is the 4th decimal place value

so n = - 4

3.04 x 10⁻⁴

3 0
3 years ago
During the holidays, Duncan works as a gift wrapper. He works 35 hours a week, spread equally over 5 workdays. If Duncan earns $
Angelina_Jolie [31]
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3 0
3 years ago
Read 2 more answers
In a bag,There are red and blue cubes in the ratio 4:7.I add 10 more red cubes to the bag.Now here are red and blue cubes in the
Hoochie [10]

Given:

The ratio of red and blue cubes is 4:7.

After adding 10 more red cubes the ratio of red and blue cubes is 6:7.

To find:

The number of blue cubes.

Solution:

The ratio of red and blue cubes is 4:7.

Let the number of red and blue cubes be 4x and 7x respectively.

After adding 10 more red cubes.

Number of red cubes = 4x+10

Then, the ratio of red and blue cubes is 6:7.

\dfrac{4x+10}{7x}=\dfrac{6}{7}

7(4x+10)=6(7x)

28x+70=42x

70=42x-28x

70=14x

Divide both sides by 14.

5=x

Now,

Number of blue cubes in the bag is

7(5)=35

Therefore, the number of blue cubes is 35.

5 0
2 years ago
C/9 - 8 = 17<br> Solve the equation and show all work please show steps!!
Amiraneli [1.4K]
<span>C/9 - 8 = 17
------------
Simplify
1/9c - 8 = 17
----------------
Add 8 to each side
1/9c - 8 + 8</span><span> </span><span>= 17 + 8
1/9c = 25
--------------------
Multiply each side by 9
9 * 1/9c = 9 * 25
c = 225</span>
5 0
3 years ago
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