Ask question

Ask question

All categories

2 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]2 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]2 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

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a

AnnZ [12381]

Response: The following comparison is made.

Detailed explanation:

At the playground, a climbing structure is 6 feet high and stretches 4 feet horizontally.

The slope can be calculated as vertical height divided by horizontal length.

$m_1$ = 6/4 = 3/2 = 1.5

In contrast, a climbing structure in the gym stands 10 feet tall, extending 6 feet horizontally.

Therefore, slope, $m_2$ = 10/6 = 5/3 = 1.67 (approximately)

As such, $m_1$ < $m_2$

Thus, the slope of the first climbing structure is less than that of the second.

5 0

2 months ago

Read 2 more answers

In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.

tester [12383]

Answer:

128

Step-by-step explanation:

Imagine you have two jars and seven marbles.

The result is $2^{7}$ .

That totals 128

3 0

1 month ago

Emerson drives 135 miles at 60 miles per hour to get to the train station. He waits 20 minutes for a train. Then he travels 350

Inessa [12570]

Response: 4.4

Detailed breakdown:

3 0

1 month ago

The bottom of Ignacio's desktop is 74.5\,\text{cm}74.5cm74, point, 5, space, c, m from the floor. Ignacio sits in his adjustable

PIT_PIT [12445]

Answer:

The inequality can be expressed as:

49.3 + 4.8r < 74.5

The solution set indicates that r < 5.25

Step-by-step explanation:

7 0

2 months ago

Your promotional budget for the year is $300 for personal selling, $300 for sales promotion, \$1,500 for advertising, and $500 f

PIT_PIT [12445]

Answer:

To determine the total promotional budget for the year, we will sum $300 for personal selling, $300 for sales promotion, $1,500 for advertising, and $500 for image promotion, which totals $2,600

8 0

1 month ago