Help asap please and thanks

3

Marianna [84]

The expression into a single logarithm is $log[(x)^{10}][(2)^{30}]$

Step-by-step explanation:

Let us revise some logarithmic rules

$log(a)^{n}=nlog(a)$
$log(ab)=log(a)+log(b)$
$nlog(a)+mlog(b)=log[(a)^{n}][(b)^{m}]$

∵ 10 log(x) + 5 log(64)

- At first re-write 10 log(x)

∴ 10 log(x) = $log(x)^{10}$

- Then re-write 5 log(64)

∴ 5 log(64) = $log(64)^{5}$

∴ 10 log(x) + 5 log(64) = $log(x)^{10}$ + $log(64)^{5}$

- Use the 3rd rule above to make it single logarithm

∵ $log(x)^{10}$ + $log(64)^{5}$ = $log[(x)^{10}][(64)^{5}]$

∴ 10 log(x) + 5 log(64) = $log[(x)^{10}][(64)^{5}]$

∵ 64 = 2 × 2 × 2 × 2 × 2 × 2

∴ We can write 64 as $2^{6}$

∴ $(64)^{5}=(2^{6})^{5}$

- Multiply the two powers of 2

∴ $(64)^{5}=(2)^{30}$

∴ 10 log(x) + 5 log(64) = $log[(x)^{10}][(2)^{30}]$

The expression into a single logarithm is $log[(x)^{10}][(2)^{30}]$

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

6 0

3 years ago

Find the average rate of change of f ( x ) = 9 x 2 − 7 on the interval [ 2 , a ] . Your answer will be an expression involving a

aleksandrvk [35]

Answer:

9a + 18

Step-by-step explanation:

so the first step is to evaluate the value of f(2).

$f(2) = 9(2)^2-7\\f(2)=9(4)-7\\f(2)=36-7\\f(2)=29$

Now that we have this value we can use the slope formula (y2 - y1) / (x2 - x1) where y2 is f(a), y1 is 29, x2 is a, and x1 is 2

$\frac{f(a)-29}{a-2}\\\\\frac{(9a^2-7)-29}{a-2}\\\frac{9a^2-36}{a-2}$

Now from here we can use long division to simplify it further

$9a^2/a = 9a\\9a(a-2)=9a^2-18a\\(9a^2-36)-(9a^2-18a)\\18a-36\\\\18a/a=18\\18(a-2)=18a-36\\(18a-36)-(18a-36)\\0\\\\9a+18$

8 0

2 years ago

Which of the statements about the y-axis are true? I.The y-axis is a vertical number line that passes through the origin.II.The

-BARSIC- [3]

Answer:

No i does not well it will be 0,5 or any other number but the x wont change

Step-by-step explanation:

5 0

3 years ago

"Statewide Insurers receives 1,600 applications per month Currently, there are 160 applications in the Reception area and 240 ap

Inessa05 [86]

Answer:

It takes 5 days to process an application.

Step-by-step explanation:

We have that number of requests per month would be equal 1600

Now, the applications in hand would be:

160 + 240 = 400

They tell us that everything must be in a number of 20 business days, therefore, the number of applications in one day would be:

1600/20 = 80

Which means that the time needed to finish an application is:

400/80 = 5 days

It takes 5 days to process an application.

4 0

4 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Darya [45]

25 is the output when the input is 4

4 0

3 years ago