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Greeley [361]
2 years ago
13

The proof for the product property of logarithms requires simplifying the expression logb(bx y) to x y. Which property is used t

o justify this step?.
Mathematics
2 answers:
Morgarella [4.7K]2 years ago
7 0

Answer:

logb(b^c)=c

Step-by-step explanation:

If you are doing this on edge it's C

masya89 [10]2 years ago
3 0

You can use the properties of logarithm to derive the simplified form of the given expression.

The simplification of the given expression requires the given below properties of logarithm

  • log_a(b^c) = c \times log_a(b)\\\\
  • log_b(b) = 1

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

  • b = log_a(c)

Some properties of logarithm are:

log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1

<h3>Using the above properties, to get to the simplified form of the given expression</h3>

The given expression is

log_b(b^{x+y})

Using the property log_a(b^c) = c \times log_a(b)\\\\, we get

log_b(b^{x+y}) = (x+y)\times log_b(b)

Using the property log_b(b) = 1, we get

log_b(b^{x+y}) = (x+y)\times log_b(b) = (x+y) \times 1 = x + y

Thus,

The simplification of the given expression requires the given below properties of logarithm

  • log_a(b^c) = c \times log_a(b)\\\\
  • log_b(b) = 1

Learn more about logarithms here:

brainly.com/question/20835449

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0.65 repeating as a decimal
vladimir1956 [14]
If .65 were to repeat it would be .656565656565656


5 0
3 years ago
The sum of the digits of a 2-digit number is 10. If 18 is added to the number, the digits of the new number are those of the ori
Aliun [14]

Answer:

46

Step-by-step explanation:

Let (ab) represent a number with a in the ten's position and b is the one's position.

This means (ab) actually has value of 10a+b.

We are given the sum of those digits of (ab) is 10; this means a+b=10.

It says if 18 is added to the number (ab), then the result is (ba).

So (ab) has value 10a+b and

(ba) has value 10b+a.

We are given then:

(ab)+18=(ba)

10a+b+18=10b+a

Subtract 10a on both sides:

b+18=10b+a-10a

Simplify:

b+18=10b-9a

Subtract b on both sides:

18=10b-b-9a

18=9b-9a

Divide both sides by 9:

2=b-a

Rearrange by commutative property:

2=-a+b

So the system of equations we want to solve is:

a+b=10

-a+b=2

-------------------------Add equations together (this will eliminate the variable a and allow you to go ahead and solve for b:

0+2b=12

2b=12

Divide both sides by 2:

b=\frac{12}{2}

Simplify:

b=6

If b=6 and a+b=10, then a=4.  a=4 since 4+6=10.

So the original number is (46).

18 more than 46 is 18+46=(64) which is what we wanted.

We also have the sum of 4 and 6 is 10 as well.

7 0
3 years ago
A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
Vlad [161]
<h3>Answer: Choice C) 31</h3>

==============================================

Explanation:

The recursive rule

f(n+1)=f(n)-3

can be rearranged to

f(n) = f(n+1)+3

after adding 3 to both sides

----------------

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

f(3) = 22+3

f(3) = 25

Repeat for n = 2

f(n) = f(n+1)+3

f(2) = f(2+1)+3

f(2) = f(3)+3

f(2) = 25+3

f(2) = 28

Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

5 0
2 years ago
(2x-7)^2 subtracted from 2
weqwewe [10]

Write out the expression 2 - (2x-7)^2.  That's it.

But if you want to go further and remove the parentheses, first expand (2x-7)^2:   (2x-7)^2 = 4x^2 - 28x + 49,

and then subtract this result from 2:

2 - (4x^2 - 28x + 49) (It's important to use parentheses here)

Now, following the distributive property of multiplication, remove the parentheses:

2 - 4x^2 + 28x - 49

Combining the constants, we get the final answer:  - 4x^2 + 28x - 47

4 0
2 years ago
How will you know that the expression is a perfect square trinomial?
Alexus [3.1K]

Answer:

An expression will be said to be a perfect square trinomial if it takes the form of ax² + bx + c and if it satisfies the condition b² = 4ac.

Step-by-step explanation:

An expression which is obtained from the square of a binomial equation is known as perfect square trinomial.

Now, the conditions for which an equation will be called a perfect square trinomial are;

i) It is of the form: ax² + bx + c

I) It satisfies the condition: b² = 4ac.

Thus, the perfect square formula could take the following forms:

(ax)² + 2abx + b² = (ax + b)²

Or

(ax)² − 2abx + b² = (ax − b)²

7 0
2 years ago
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