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13 days 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 [3.9K]13 days 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 [3.9K]13 days 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.

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The value of y at x=-1in the equation 5y=2 is

Zina [3917]

Answer: y = 2/5 --> y = 0.4

Step-by-step explanation:

The equation 5y = 2 represents a horizontal line at y = 2/5.

This means that the y-coordinate holds the value of 2/5 = 0.4 for any x-coordinate.

7 0

17 days ago

Brad buys a pack of 12 bottles of energy drink for £9.25 he then sells all bottles for £1 each. Work out brads percentage profit

Svet_ta [4341]

La ganancia de Brad fue del 30%

Explicación adicional:

La ganancia es el dinero obtenido al vender un producto por encima de su costo original.

La fórmula para calcular la ganancia es:

$Profit= Selling\ price-Purchase\ price$

Datos:

Precio de compra del paquete de bebidas energéticas = £9.25

Precio de venta por botella = £1

Precio total por 12 botellas = 1 * 12 = £12

Ganancia = Precio de venta - Precio de compra

= 12 - 9.25

= £2.75

Así, la ganancia de Brad fue de £2.75

Luego,

Porcentaje de ganancia = (Ganancia / Precio de compra) * 100

= (2.75 / 9.25) * 100

= 0.30 * 100

= 30%

La ganancia de Brad fue del 30%

Palabras clave: Ganancia, pérdida

Aprende más sobre ganancia y pérdida en:

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3 0

14 days ago

Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 mi

Leona [4187]

Let's sketch the triangle.

The sides are a= 37.674 miles

b= 11.164 miles

c= 36.318 miles

We'll apply the cosine rule for angle calculations

(since the sine law cannot be employed without knowing any angle measurements).

The cosine law is given by

$c^{2} = a^{2} +b^{2} -2ab cos C$

Substituting the values results in

$(36.318)^{2} = (37.674)^{2} + (11.164)^{2} - 2(37.674)(11.164). Cos C$

$1318.997 = 1419.33 + 124.634 - 841.184. Cos C$

$1318.997 = 1543.964 - 841.184. Cos C$

$841.184. Cos C = 1543.964-1318.997$

$841.184. Cos C = 224.967$

$Cos C = \frac{224.967}{841.184}$

$cos C = 0.267$

C = 74.48°

We can find angle A using the sine law

$\frac{a}{SinA} = \frac{c}{Sin C}$

$\frac{37.674}{Sin A} = \frac{36.318}{Sin 74.48}$

$Sin A = \frac{37.674. sin 74.48}{36.318}$

$Sin A = \frac{37.674 X 0.963}{36.318}$

$Sin A = 0.998$

A= $sin^{-1} (0.998)$

A = 87.38°

The third angle B can be determined by calculating 180° minus the sum of angles A and C

$B = 180-(74.48 + 87.38)$

B = 180 - 161.86

B = 18.14°

Thus, we have calculated all three angles (as shown in the attached figure).

7 0

6 days ago

The height of an arrow shot upward can be given by the formula s = v0t - 16t2, where v0 is the initial velocity and t is time. H

Svet_ta [4341]

The arrow reaches a height of 48 feet at about 0.55 seconds and again at approximately 5.45 seconds.

Explanation

The formula provided is: $s=V_{0}t-16t^2$

Given the initial velocity as 96 ft/s, we have $V_{0}=96$

To determine when the arrow attains a height of 48 feet, substitute $s= 48$ into the formula:

$48=96t-16t^2\\ \\ 16t^2-96t+48=0\\ \\ 16(t^2-6t+3)=0\\ \\ t^2-6t+3=0\\ \\ t^2-6t =-3\\ \\ t^2-6t+9=-3+9\\ \\ (t-3)^2 = 6\\ \\ t-3= \pm \sqrt{6} \\ \\ t=3\pm \sqrt{6}\\ \\ t = 5.45 , 0.55$

Therefore, the arrow is at 48 feet height at roughly 0.55 seconds and again at 5.45 seconds.

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13 days ago

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The owner of a skate shop notices that every time a certain employee has a shift, there are higher sales numbers at the end of t

zzz [4035]

Response:

Correlation.

In-depth explanation:

When the goal is to determine the connection between two or more variables to assess the impact of one variable (the independent one) on another variable (the dependent one), this is referred to as a correlation study or analysis. In this case, the link between employee shifts and sales or productivity is analyzed; it shows how the number of shifts worked by a specific employee correlates positively with the revenue generated. Here, the shift worked by the employee acts as the independent variable while the generated revenue is the dependent one.

6 0

16 days ago