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3 years ago

Solve and type in a different form by using the given theorems of logarithms. log N^3

Mathematics

2 answers:

Kipish [7]3 years ago

8 0

<h3><u>Answer:</u></h3>

Hence, the different form of log N^3 by using the given theorems of logarithms is:

$\log N^3=3\log N$

<h3><u>Step-by-step explanation:</u></h3>

We have to represent the given logarithmic function in some other form using the property of logarithm.

We are given a logarithmic function as:

$\log N^3$

As we know the property of logarithm that:

$\log m^n=n\log m$

Hence, we can represent our given function as:

$\log N^3=3\log N$

Hence, the different form of log N^3 by using the given theorems of logarithms is:

$\log N^3=3\log N$

timofeeve [1]3 years ago

5 0

Log N^3 = 3 log N

using the theorem log a^2 = 2 log a

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Evaluate 14 – 4 – 2h when p=1 and h=4.

ki77a [65]

Answer:

14 – 4 – 2h = 2

Step-by-step explanation:

14 – 4 – 2h

fill in 4 for h

14 - 4 - 2(4)

14 - 4 - 8

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2 years ago

What is the solution to the equation 1/square root of 8 = 4^(m + 2)?

Digiron [165]

Take the log (base 4) of both sides of the equation.
$\log_{4}(\frac{1}{\sqrt{8}}) = m + 2$
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$-2 \frac{3}{4}= m$

The appropriate choice is ...
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3 years ago

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4. Is rap music more popular among young Indians than among young Asians? A sample survey compared 634 randomly chosen Indians a

bulgar [2K]

Answer:

H0 is accepted

there is no difference between the proportions of Indian and Asian young people who listen to rap music every day.

Step-by-step explanation:

Given a sample survey compared 634 randomly chosen Indians aged 15 to 25 with 567 randomly selected Asians in the same age group.

$p_{1} = \frac{368}{634} =0.580$

It found that 368 of the Indians and 130 Asians listened to rap music every day.

$p_{2} = \frac{130}{567} =0.229$

Null hypothesis H0: there is no difference between the proportions of Indian and Asian young people who listen to rap every day.

$p_{1} = p_{2}$

Alternative hypothesis:- $p_{1} \neq p_{2}$

Level of significance α = 0.05

The test of statistic

$z = \frac{p_{1} - p_{2}}{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} }) } } }$

where $p = \frac{n_{1}p_{1} + n_{1}p_{2}}{n_{1}+n_{2}} = \frac{634(0.580)+567(0.229)}{634+567}$

p = 0.414

and q = 1-p = 1- 0.414 =0.586

$Z = \frac{0.580-0.229}{\sqrt{0.414(0.586)(\frac{1}{634} +\frac{1}{567} } } }$

on calculation , we get

z = 0.300 ><1.96 at 95 % level of significance

H0 is accepted

there is no difference between the proportions of Indian and Asian young people who listen to rap every day.

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3 years ago

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lora16 [44]

Can you please include a question please? Thank you

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3 years ago

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Factor the expression below 36a2-25b2 which binomial is factor of the expression

Serhud [2]

Answer: (6a + 5b) • (6a - 5b)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(36 • (a2)) - 52b2

Step 2 :

Equation at the end of step 2 :

(22•32a2) - 52b2

Step 3 :

Trying to factor as a Difference of Squares :

3.1 Factoring: 36a2-25b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check : 25 is the square of 5

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (6a + 5b) • (6a - 5b)

Final result :

(6a + 5b) • (6a - 5b)

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3 years ago

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