4. (-5, 2) and (-5, 6)

write the logarithm as a sum or difference of logarithms. simplify each term as much as possible. log4(6ab)

Dominik [7]

The logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

<h3>Simplifying Logarithms</h3>

From the question, we are to write the given logarithm expression as a sum or difference of logarithms

The given logarithm is

$log_{4 }6ab$

This can be written as

$log_{4 }6 \times a \times b$

From one of the rules of logarithm, we have that

$log_{x }yz= log_{x }y + log_{x }z$

Thus,

$log_{4 }6 \times a \times b$ becomes

$log_{4 }6 + log_{4 }a + log_{4 }b$

This can be further simplified into

$log_{4 }3 \times 2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b$

If desired, this can be further simplified into

$log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b$

$\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Hence, the logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Learn more on Simplifying logarithms here: brainly.com/question/17851187

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8 0

1 year ago

What is the reason that m<2 and m<3 are supplementary

katen-ka-za [31]

Answer:

see explanation

Step-by-step explanation:

∠2 and ∠3 are same- side interior angles and are supplementary.

6 0

2 years ago

A wallet contains $460 in $5, $10, and $20 bills. The number of $5 bills exceeds twice the number of $10 bills by 4, and the num

Butoxors [25]

Answer:

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

Step-by-step explanation:

Let x number of $5, y number of $10 and z number of $20

The number of $5 bills exceeds twice the number of $10 bills by 4.

Therefore, x = 2y + 4

The number of $20 bills is 6 fewer than the number of $10 bills.

Therefore, z = y - 6

A wallet contains $460 in $5, $10, and $20 bills.

Therefore,

5x + 10y + 20z = 460

Substitute x and y into equation

5(2y+4) + 10y + 20(y-6) = 460

10y + 20 + 10y + 20y - 120 = 460

40y - 100 = 460

40y = 460 + 100

40y = 560

y = 14

Put the value of y into x = 2y + 4 and solve for x

x = 2(14) + 4

x = 32

Put the value of y into z = y - 6 and solve for z

z = 14 - 6

z = 8

Hence, the each type of bills,

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

3 0

3 years ago

Read 2 more answers

Drew wrote the

Fiesta28 [93]

Every number consists of digits. One digit is the least number of digits a number can have. The place value is the position of each digit in a number. <span>Digits are separated into groups of three by commas. So, a period is a group of three digits, but not any three digits. So, Drew's sentence is false. A period is a group of consecutive digits.</span>

4 0

3 years ago

I thought of a number, then divided it by another number, and got a result of 7. Think of the possible values for my number and

allsm [11]

Let the first unknown number be $x$
And the second unknown number be $y$

We know that $x$ ÷ $y$ = 7

My number is a multiple of 7 and also multiple of $y$
This is because of 7 × $y$ = $x$
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The number I divided my number by can be any number but ZERO
Because $x$ ÷ 0 is undefined
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My number cannot be a number which we cannot divide by SEVEN
Because $x$ ÷ $y$ = 7, so $x$ must be divisible by 7 to obtain $y$

$\frac{x}{y} =7$
$\frac{x}{7} =y$
$7y=x$

4 0

3 years ago