Approximate the logarithm using the properties of logarithms, given logb 2 ≈ 0.3562,
logb 3 ≈ 0.5646,
and
logb 5 ≈ 0.8271.
(Round your answer to four decimal places.)
㏒b(2b^3)
Answers
Final answer:
By using the properties of logarithms, namely ㏒b(a * c) = ㏒b(a) + ㏒b(c) and ㏒b(a^p) = p * ㏒b(a), we find the approximation of the logarithm ㏒b(2b^3) to be 3.3562.
Explanation:
To approximate the value of ㏒b(2b^3), we can use the properties of logarithms. The first one is that ㏒b(a * c) = ㏒b(a) + ㏒b(c), where a and c are the numbers we wish to find the logarithm of. We can apply this property to your given expression as follows:
- ㏒b(2b^3) = ㏒b(2) + ㏒b(b^3).
The second logarithmic property we need is that ㏒b(a^p) = p * ㏒b(a), where a is the base, and p is the exponent. We can apply this property to the second term on the right side:
- ㏒b(b^3) = 3 * ㏒b(b).
- Since ㏒b(b) is equal to 1 (because b raised to the power of 1 is b), then our equation becomes:
- ㏒b(2b^3) = ㏒b(2) + 3.
Now, we can substitute the values given for ㏒b(2), which is 0.3562:
- ㏒b(2b^3) = 0.3562 + 3 = 3.3562.
So, approximating ㏒b(2b^3) to four decimal places, we get 3.3562.
Learn more about Logarithms here:
#SPJ3
que representa Laos hombres con relacion al total
Related Questions
A company builds a new wing for its east branch and knows that each additional room will gain $1200 of profit. The construction company will cost $44,000 to construct the wing.How many rooms are need to break even? (Hint: You must PAY the fee to the construction company.)If you wanted to make twice as much profit as you spent, how many rooms would need to be built?
What is the purpose of proof in mathematics?
A cylinder has a height h, and a radius (3h-2)The area of the base is pi (3h-2)^2 The volume of the clinder is V= pi(3h-2)^2h 10. Multiply the polynomials to simplify the expression for the volume: V=pi(3h-2)^2h by
Mary is having a party at the park. She is going to spend $438.The cost to rent the shelter is $15 plus food is going to cost $6per person. How many people is she having?
mixture of red and gold beads that she can sell for $2
an ounce. The solution of the system shows the
number of beads needed for Juanita to break even.
x + y = 12
x + 3y = 24
How many ounces of red beads will Juanita buy to
break even?
How many ounces of gold beads will she buy?
Answers
Answer:
6 ounces of red beads
6 ounces of gold beads
Step-by-step explanation:
x + y = 12
x + 3y = 24
We can solve this with substitution or elimination. In this case, I would suggest elimination. Subtract the first equation from the second:
2y = 12
y = 6
Plug back into either equation to find x.
x = 6
Answer:
How many ounces of red beads will Juanita buy to break even?
6
How many ounces of gold beads will she buy?
6
Step-by-step explanation:
Because I got 100 percent on EDG 2020
Answers
Answer:
y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]
Step-by-step explanation:
y" - y' - 2y = 5e⁻ᵗ
The total solution of this differential equation will be a sum of its complimentary and particular solutions.
y = y꜀ + yₚ
The complimentary or homogenous solution is a solution of
y" - y' - 2y = 0
y꜀ = Ay₁ + By₂
Solving this part in the attached image, we obtain
y₁ = e⁻ᵗ and y₂ = e²ᵗ
The particular solution can be obtained using the method of variation of parameters and the method of undetermined coefficients.
The method of variation of parameters is used and explained in the page 1, 2 and page 3 of the attached images.
The method of undetermined coefficients is then used to check if the solution obtained is correct.
With y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)],
y' and y'' were obtained and put in the equation, and the answer obtained was 5e⁻ᵗ.
So, Proved!
y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]
Hope this helps!!!
Answers
First find the area of the circle
Area = πr^2
=3.14 x 16
50.24 cm^2
But here we need the area of the semicircle
so 50.24/2 = 25.12 cm^2
Now we find the area of the triangle
Area = 1/2bh
= 1/2 x 8 x 4
16 cm^2
The area of the shaded region = 25.12-16
= 9.12 cm^2
Hope this helps you!
Answers
2.357 divided by 21= 17
3. 1215 divided by 15= 81
4.360 divided by 24= 15
Answer:
51.111, 17, 81, 15
Step-by-step explanation:
Answers
Answer:
Answer above is correct!
First Box: 4
Second Box: -16
Step-by-step explanation:
Hope this helps :D
Answer:
Step-by-step explanation:
A line that is parallel to the line that goes through (-3, -3) and (-1, 5) will have the same slope as the one we will find when we plug those numbers into the slope formula. Let's do that first:
so the line we need to write has a slope of 4. Moving on...
If the x-intercept we need is 4, that means that we need to understand what an x-intercept is. The x-intercept exists where y = 0; so what we need to do is to write the equation of the line that has a slope of 4 and passes through the point (4, 0). Doing that:
y - 0 = 4(x - 4) and
y = 4x - 16
Answers
Answer:
kya pls help meeeeeeeeeeeeeeee.
please thanks and follow me.