Ask question

Ask question

All categories

mihalych1998 [28]

4 years ago

11

Rewrite the following expression using the properties of logarithms. log2z+2log2x+4log9y+12log9x−2log2y

1 answer:

kramer4 years ago

5 0

Use the rules of logarithm:
1. log(x)+log(y)=log(xy)
log(x)-log(y)=log(x/y)
2. k*log(x) = log(x^k)
log(x)/k = log(x^(1/k))

<span>log(2z)+2log(2x)+4log(9y)+12log(9x)−2log(2y)
=</span>log(2z)+log(4x^2)+log(9^4y^4)+log(9^12x^12)−log(4y^2)
=log(2z)+log(4x^2)+log(6561y^4)+log(282429536481x^12)−log(4y^2)
=log(59296646043258912 * x^14 * y^6 * z)

You might be interested in

Select all the pairs of equivalent expressions.

iren2701 [21]

Answer:

$\huge\boxed{(3^4)^4=3^8\cdot3^8}\\\boxed{4^3\cdot5^3=20^3}\\\boxed{(4^3)^3=4^3\cdot4^3\cdo4^3}$

Step-by-step explanation:

$a^n\cdot a^n=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}\\\\(a\cdot b)^n=a^n\cdot b^n\\=====================$

$(4^3)^3=4^{3\cdot3}=4^9\\4^3\cdot4^3=4^{3+3}=4^6\\\\4^9\neq4^6\to(4^3)^3\neq4^3\cdot4^3\\==================$

$(3^4)^4=3^{4\cdot4}=3^{16}\\3^8\cdot3^8=3^{8+8}=3^{16}\\\\(3^4)^4=3^8\cdot3^8\\================$

$6^4\cdot3^4=(6\cdot3)^4=18^4\\\\18^4\neq18^8\to6^4\cdot3^4\neq18^8\\=================$

$4^3\cdot5^3=(4\cdot5)^3=20^3\\\\4^3\cdot5^3=20^3\\=================$

$(4^3)^3=4^{3\cdot3}=4^9\\4^3\cdot4^3\cdot4^3=4^{3+3+3}=4^9\\\\(4^3)^3=4^3\cdot4^3\cdot4^3$

3 0

3 years ago

Which expression is equivalent to (f + g)(4)?

ddd [48]

(f + g)(x) = f(x) + g(x) therefore (f + g)(4) = f(4) + g(4)

3 0

3 years ago

Read 2 more answers

Tina sends 12 text messages each day in June. A mobile phone company offers two packages. Package A: The first 100 texts each mo

Mnenie [13.5K]

Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.

Tina sends 12 text messages each day in June

June has 30 days, so in June, Tina sent 12*30 = 360 text messages.

Package A:

First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.

She sends 360 messages, with:

The first 100 costing 3p.

The next 100 costing 2p.

The final 360 - 200 = 160 costing 1p.

She pays:

$100*3 + 100*2 + 160*1 = 660$

Package B:

2p for each message, 360 messages, so:

360*2p = 720p.

Which package is better?

Package A costs less, thus, it offers her the better value for money in 30 days.

Another example of a problem in which a person has to choose between two packages is given in brainly.com/question/10693932

6 0

3 years ago

The table shows one point from the given graph. How could you find more ordered pairs to create a graph and table of equivalent

11Alexandr11 [23.1K]

Answer:

A,B,D

Step-by-step explanation:

JUST TOOK THE QUIZ

3 0

3 years ago

Read 2 more answers

Mount McKinley, the highest mountain in North

riadik2000 [5.3K]

Since the deepest point of Death Valley is below sea level, its altitude is negative. So, the difference between the altitudes is

$20320-(-280)$

Subtracting a negative means to add, so we have

$20320-(-280)=20320+280=20600$

4 0

3 years ago