Ask question

Ask question

All categories

3 months ago

5

Explain the error in the solution below. What additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x

= log533 x = 27

2 answers:

PIT_PIT [12.4K]3 months ago

5 0

The mistake lies in the fact that the logarithms have different bases. The one-to-one property of logarithms cannot be applied unless the bases are identical. <span>To correct this, the change of base formula should be used to express the logarithms with a uniform base.
I have confirmed this using Edge.</span>

tester [12.3K]3 months ago

5 0

Answer:

The error occurs at step 3,

Steps 4 through 9 provide the proper correction.

Detailed explanation:

Given the solution below,

$\log x -\log_5 3 = 2\log_5 3\\\log x = 3\log_5 3\\\log x = \log_5 33\\x = 27$

Task: Identify the error and determine the necessary additional step.

Solution: The fault is in step 3 and a further step must be inserted afterwards.

We proceed as follows:

Step 1 - $\log x -\log_5 3 = 2\log_5 3$

Step 2 - $\log x = 3\log_5 3$

Step 3 - $\log x =\log_5 3^3$

Step 4 - $\log x=\log_5 27$

By applying the change of base rule for logarithms,

$\log_b a=\frac{\log a}{\log b}$

Step 5 - $\log x=\frac{\log 27}{\log 5}$

Step 6 - $\log x=\frac{1.431}{0.698}$

Step 7 - $\log x=2.050$

Step 8 - $x=10^{2.050}$

Step 9 - $x=112.20$

The steps from 4 to 9 represent the correct procedure.

You might be interested in

The Multiplication Rule says that P(A and B) = P(A) × P(B). What must be true about events A and B for this rule to apply?

Svet_ta [12734]

Response:

Events A and B exhibit independence.

Detailed explanation:

We are provided with

The multiplication principle applicable to events A and B

$P(A\cap B)=P(A)\times P(B)$

A correct assertion regarding events A and B is necessary for this principle to hold.

It is understood that for two events A and B to be independent

Consequently, the probability

$P(A\cap B)=P(A)\cdot P(B)$

Thus, the correct assertion concerning events A and B for the application of this principle is stated as

Events A and B are independent.

7 0

2 months ago

An automotive manufacturer has developed a new type of tire that the research team believes to increase fuel efficiency. the man

PIT_PIT [12445]

Answer:

3) One-sided, compare two populations

Step-by-step explanation:

A manufacturer intends to evaluate if there is an improvement in the average gas mileage among mid-sized sedans that use a new type of tire, in comparison to those that do not utilize this tire type.

Thus, we have two distinct populations:

Population 1: Mid-sized sedans equipped with the new tire.

Population 2: Mid-sized sedans without the new tire.

Consequently, a comparison is being made between these two populations.

Furthermore, the manufacturer aims to determine if there is an enhancement in average gas mileage. As such, the alternative hypothesis will be right-tailed, indicating it is a one-sided test.

6 0

3 months ago

What is the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008 . What might have been the

AnnZ [12381]

Answer:

The exact population of Vermont in 2008 could have been around 618,000

Step-by-step explanation:

* Here's how rounding to the nearest ten thousand works:

- Numbers ending with the last four digits between 0001 and 4999 are rounded down to the nearest lower multiple of ten thousand

- Example: 83,525 rounds down to 80,000.

- If the last four digits are 5000 or above, round up to the next higher ten thousand

- Example: 58,988 rounds up to 60,000

* Applying this rule to the problem given:

Since the rounded population is 620,000 to the nearest ten thousand, the actual population could be any value with the last four digits from 0001 to 4999 (like 618,000) or from 5000 upwards (like 624,000).

Therefore, 618,000 might represent the actual population of Vermont in 2008

6 0

3 months ago

What is the factored form of a2 – 121?

AnnZ [12381]

Response:

The factored expression $a^2-121$ is $(a+11)(a-11)$ .

Detailed explanation:

Provided: $a^2-121$

Our goal is to express the given equation in a factored form.

Factoring pertains to rewriting an expression so that the product of its factors yields the original expression

Let’s consider the expression $a^2-121$ .

We recognize the algebraic identity $x^2-y^2=(x+y)(x-y)$

Thus, we have $a^2-121=a^2-(11)^2$ .

Matching with the above identity, we assign x= a, and b = 11, leading to

$a^2-(11)^2=(a+11)(a-11)$ .

Consequently, the factored expression $a^2-121$ is $(a+11)(a-11)$ .

7 0

1 month ago