Which of the following requires a proof?

. Write each number in terms of natural logarithms, and then use the properties of logarithms to show that it is a

siniylev [52]

Answer:

The answer is 3/4

Step-by-step explanation:

Hi, we need to change the base of the logarithm, for that we need to use the following formula.

$Log_{b} (a)=\frac{Ln(a)}{Ln(b)}$

In our case, this is:

$Log_{9} (\sqrt{27} )=\frac{Ln(\sqrt{27} )}{Ln(9)}$

Which is the same as:

$\frac{Ln(27)^{\frac{1}{2} }}{Ln(9)}$

Now, let´s solve this using the log properties

$\frac{1}{2} (\frac{Ln(27)}{Ln(9)} )$

$\frac{1}{2} (\frac{Ln(9*3)}{Ln(9)} )$

$\frac{1}{2} (\frac{Ln(9)+Ln(3)}{Ln(9)} )$

$\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(3)}{Ln(9)} )\\$

We can change 3 for 9^(1/2)

$\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9^{\frac{1}{2} } )}{Ln(9)} )\\$

$\frac{1}{2} (\frac{Ln(9)}{Ln(9)}+\frac{Ln(9 )}{2*Ln(9)} )\\$

Since Ln(9) / Ln(9) =1, we get.

$\frac{1}{2} (1+\frac{1}{2} )$

$\frac{1}{2} (\frac{3}{2} )=\frac{3}{4}$

Best of luck.

4 0

3 years ago

WILL MARK BRANLIESTTT<br> What is the value of x?<br> A. 42°<br> B. 48<br> C. 64°<br> D. 84

valkas [14]

Answer:

Step-by-step explanation:

<u>*It's an isosceles triangle so 2 of the angles are going to be the same degrees</u>

<u>*Every triangle is 180 degrees</u>

(48)+(48)=96 then 180-96=84

8 0

3 years ago

What times what equals 225?

defon

I got 5 times 45 because I multiplied by 5 to get my answer.

4 0

4 years ago

Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The

Travka [436]

Answer:

Aidan is 2 miles far from the ending point when he reaches the water station.

Step-by-step explanation:

The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:

From starting point to ending point:

$D = \sqrt{(3-3)^{2}+(9-1)^{2}}$ (Eq. 1)