Mathematics, 09.04.2020 22:11 Benjamincompton07

Identify the properties used to perform the following simplifications:
Q1) log(100) = log(400) - log(4)
Q2) log(x^2) = log(x) + log(x)
Q3) log(49) = 2log(7)
Q4) Which properties would you use to simplify the following expression?
log (17x^3) two properties

Properties:
1. log(xy) = logx + logy

2. log(x/y) = logx − logy

3. log(x^r) = r logx

Answers: 2

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Answers

Answer from: BreBreDoeCCx

Property

Q1) log(100) = log(400) - log(4) ↔ 2. $\log (x/y)=\log x - \log y$

Q2) log(x²) = log(x) + log(x) ↔ 1. $\log (xy)=\log x+\log y$

Q3) log(49) = 2log(7) ↔ 3. $\log (x^r)=r\log x$

Q4) Which properties would you use to simplify the following expression? log (17x³):

1. $\log (xy)=\log x+\log y$ , and 3. $\log (x^r)=r\log x$

Explanation:

Properties

1. $\log (xy)=\log x+\log y$

This property means that the logarithm of a product is equal to the sum of the logariths of the factors.

x² may be written as the product x · x

Then, the logarithm of x² is the same that the logarithm of x · x

And you can apply the rule of the logarithm of a product:

log(x²) = log (x·x) = log(x) + log(x)

Hence, the property applied to Q2) is the number 1.

2. $\log (x/y)=\log x - \log y$

This property states that the logarithm of a quotient is equal to the logarithm of the dividend less the logarithm of the divisor.

The number 100 can be written as the quotion 400/4. Then:

log(100) = log (400/4)

And, by the second property:

log(400/4) = log(400) - log(4)

Thus, the property use to simplify the Q1) is the number 2.

3. $\log (x^r)=r\log x$

This property states that the logaritm of a power is equal to the exponent multiplied by the logarithm of the base

Then, since 49 = 7², you can write:

log (49) = log (7²)log (7²) = 2 × log (7) = 2log(7)

Therefore, the property used to perform the simplification of Q3) is the third one.

Q4)

The given expression, log (17x³,) is the logarithm of a product: the product of 17 and x³.

Thus, you apply the property number 1:

log (17x³) = log (17) + log(x³)

Now, you can simplify the second term: since x³ is a power you can use the property number 3, logarithm of a power, to find:

log(x³) = 3log(x)

Then, the expression simplified is:

log(17x³) = log(17) + 3log(3), for which you had to use two properties of the logarithms: number 1, and number 3.

Answer from: Quest

according to egenuity the answer is

step-by-step explanation:

d. 344.22

Answer from: Quest

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

there is a hike in both the graphs so the graphs are increasing on their domain.x-intercept of log x and log 6x are differentthere is a vertical asymptote of both the graphs so there is no y-interceptas both the graphs are increasing so there is no horizontal asymptote

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Identify the properties used to perform the following simplifications:
Q1) log(100) = log(400)...