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Alborosie
3 years ago
5

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

ultipal of logarithms.See example 3.
In(x x^2 + 1^1/2)
Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

Answer:

\ln x+\frac{1}{3}\ln (x^2+1)

Step-by-step explanation:

Consider the given expression is

\ln (x\sqrt[3]{x^2+1})

We need to rewrite the expression as a sum,difference,or multiple of logarithms.

\ln (x(x^2+1)^{\frac{1}{3}})        [\because \sqrt[n]{x}=x^{\frac{1}{n}}]

Using the properties of logarithm we get

\ln x+\ln (x^2+1)^{\frac{1}{3}}         [\because \ln (ab)=\ln a+\ln b]

\ln x+\frac{1}{3}\ln (x^2+1)        [\because \ln (a^b)=b\ln a]

Therefore, the simplified form of the given expression is \ln x+\frac{1}{3}\ln (x^2+1).

You might be interested in
For what value of x is the parallelogram a rhombus.
Stells [14]

Answer:

Step-by-step explanation:

2 × ( 3x + 6 )° + ( 16x + 14 )° = 180°

22x + 26 = 180

22x = 154

x = 7

4 0
3 years ago
if your average stride length is 2.6 feet how many strides will it take you to walk to grandparents house
IceJOKER [234]

The distance from your house to your grandparents house is 3.67 miles or 19377.6 ft.

So the total number of strides needed would be:

strides needed = 19377.6 ft / (2.6 ft / stride)

<span>strides needed = 7,452.92 = 7,453 strides</span>

3 0
4 years ago
There are two numbers, one is 7 more than twice the other. The sum of the numbers is 43. Make the equation to find the smaller n
Mrrafil [7]

Answer:

Smaller number: 12

Greater number: 31

Step-by-step explanation:

Hi there!

Let x equal to the smaller number.

Let y be equal to the greater number.

<u>1) Translate the information into equations</u>

"One is 7 more than twice the other"

⇒ y=2x+7

"The sum of the numbers is 43"

⇒ x+y=43

<u>2) Use substitution to solve for the smaller number</u>

x+y=43

Plug the equation y=2x+7 into the above equation

x+(2x+7)=43\\x+2x+7=43\\3x+7=43

Subtract both sides by 7

3x+7-7=43-7\\3x=36

Divide both sides by 3 to isolate x

\frac{3x}{3} = \frac{36}{3} \\x=12

Therefore, the smaller number equates to 12.

<u>3) Use substitution to solve for the greater number</u>

x+y=43

Plug in x as 12

12+y=43

Subtract both sides by 12 to isolate y

12+y-12=43-12\\y=31

Therefore, the greater number equates to 31.

I hope this helps!

3 0
3 years ago
13. Suppose the probability of passing a driving test is 65%. (a) On a certain afternoon 15 people are tested. (i) What is the e
Alex_Xolod [135]

Answer: 9

Step-by-step explanation:

Based on the information given in the question, the expected number of people who pass will be calculated as:

= Probability of passing the driving test × Number of people tested

= 65% × 15

= 0.65 × 15

= 9.75

Therefore, expected number of people who pass is 9.

8 0
3 years ago
A physical trainer decides to collect data to see if people are actually weight changing weight during the shelter in place. He
telo118 [61]

Answer:

H0: µd = 0 (claim)

H1: µd ≠ 0

This is a two-tail t-test for µd

Step-by-step explanation:

This is a paired (dependent) sample test, with its hypothesis is written as :

H0: µd = 0

H1: µd ≠ 0

From the equality sign used in the hypothesis declaration, a not equal to ≠ sign in the alternative hypothesis is used for a two tailed t test

The data isn't attached, however bce the test statistic cannot be obtained. However, the test statistic formular for a paired sample is given as :

T = dbar / (Sd/√n)

dbar = mean of the difference ; Sd = standard deviation of the difference.

3 0
3 years ago
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