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3 years ago

1) write the expression as a single logarithm log3 40 - log3 10 show work. 2) solve the exponential equation 1/16 =64^[4x-3]

1 answer:

7 0

1) The expression log3(40) - log3(10) can be simplified. When substracting logs with the same base values, in this case 3, you can simplify the expression by dividing the species inside each log.

log3(40) - log3(10)
log3(40/10)
log3(4) = simplified expression

2) To solve the exponential equation 1/16 = 64^(4x-3) we can also simplify things first. 16 = 4², and 64 = 4³.

1/4² = 4³⁽⁴ˣ⁻³⁾
4⁻² = 4³⁽⁴ˣ⁻³⁾

At this stage since the bases are equal, the exponents must also be equal.

-2 = 3(4x-3)
-2/3 = 4x - 3
4x = 7/3
x = 7/12

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Simplify. (-2)^-3<br> A.-8<br> B.-1/8<br> C.1/8<br> D.8

DiKsa [7]

ANSWER

${( - 2)}^{ - 3} =- \frac{1}{ 8}$

EXPLANATION

We want to simplify;

${( - 2)}^{ - 3}$

Recall that,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

${( - 2)}^{ - 3} = \frac{1}{{( - 2)}^{ 3}}$

We multiply out to get,

${( - 2)}^{ - 3} = \frac{1}{{- 2} \times - 2 \times - 2}$

${( - 2)}^{ - 3} = \frac{1}{ - 8}$

The correct choice is B.

6 0

3 years ago

David y Almudena tienen entre los dos 225 euros. Calcula cuánto dinero tiene cada uno si Almudena posee 75 euros más que David.

Misha Larkins [42]

David and Almudena have between the two 225 euros. Calculate how much money each has if Almudena has 75 euros more than David.

For this case we propose a system of equations:

x: Let the variable that represents Almudena's amount of money

y: Let the variable that represents David's amount of money

According to the statement we have:

$x + y = 225\\y + 75 = x$

Substituting the second equation into the first:

$y + 75 + y = 225\\2y + 75 = 225\\2y = 225-75\\2y = 150\\y = \frac {150} {2}\\y = 75$

We find the value of the variable x:

$x = 75 + 75 = 150$

Almudena has 150 euros

David has 75 euros

Answer:

Almudena has 150 euros

David has 75 euros

3 0

4 years ago

HELP ME I WILL GIVE BRANLISEST

RoseWind [281]

Answer:

i think it

Step-by-step explanation:

6 0

3 years ago

Property taxes are based on the value of the property

Svetllana [295]

Based on the calculations, the average selling price for these properties is equal to $127,865.

<h3>How to determine the average selling price?</h3>

Mathematically, the average selling price for these properties would be calculated by using the following formula:

Average price = [F(x)]/n

<u>Note:</u> The total number of properties is equal to 5.

Substituting the given parameters into the formula, we have;

Average price = [118,450 + 126,500 + 128,000 + 130,425 + 135,950]/5

Average price = 639,325/5

Average price = $127,865.

Read more on average price here: brainly.com/question/14409137

#SPJ1

<u>Complete Question:</u>

Property taxes are based on the value of the property. city officials use the average selling price of similar properties to estimate the value. the selling prices of similar properties are listed below. $118,450 $126,500 $128,000 $130,425 $135,950. What is the average selling price?

7 0

2 years ago

0.39<br> which is best buy<br> 0.41<br> 0.4.

Nana76 [90]

Answer:

0.39 because it's the cheapest / least

Step-by-step explanation:

Ok so we are trying to find the least. So first line up your decimals as shown below

<u>Tens</u> <u>Tenths</u> <u>Hundredths</u>

<h3> 0 . 3 9</h3><h3>---------------------------------------</h3><h3> 0 . 4 1</h3><h3>---------------------------------------</h3><h3> 0 . 4 0 ---> Imaginary 0</h3><h3 />

Now fill in any empty spaces with a 0 as shown in the decimal 0.4, your decimal will still have the same amount because 0.4 = 0.40 = 0.400 no matter how many 0's you put in the decimal.

When your done with placing 0's, look at the numbers in the first column, the Tens column. As you can see we have the numbers 0, 0, 0. They're all the same so we don't have to worry about that. Now lets go to the next column, the Tenths column. We have the numbers 3, 4, 4. Remember, we are finding the least amount. we know 3 is less than 4 so the decimal with the 3 in the Tenths place is the best buy. If these numbers were the same we would go on to the next place, the Hundredths place. If 2 of the decimals had a 3 in the Tenths place, you would eliminate the decimal with no 3 in the Tenths place and go on to the next place using only the decimals you have left.

So, <em>0.39</em> is the best buy.

Hope this helps you and makes Sense! :)

This is NOT copy pasted, I actually wrote all of this so that the person reading this answer can understand what I'm trying to explain.

Thank you, and have a Great Day! ;)

5 0

3 years ago