All categories

3 years ago

Simplify: log81/8 + 2log2/3 - 3log 3/2 +log 3/4

Mathematics

1 answer:

MissTica3 years ago

5 0

Answer:

Step-by-step explanation:

Using the laws of logarithms:

log81/8 + 2log2/3 - 3log 3/2 + log 3/4

= log 81/8 + log (2/3)^2 - log (3/2)^3 + log 3/4

= log 81/8 + log 4/9 - log 27/8 + log 3/4

= log 81/8 + log 4/9 - (log 27/8 - log 3/4)

= log (81/8 * 4/9) - log (27/8 * 4/3)

= log 9/2 - log 9/2

= 0.

You might be interested in

Use De Moivre’s Theorem to compute the following: <img src="https://tex.z-dn.net/?f=%5B3%28cos27%2Bisin27%29%7D%5E5" id="TexForm

zhannawk [14.2K]

Hello:
<span>Use De Moivre’s Theorem :
</span>(3(cos27 +isin27)^5 = 3^5( cos(27 × 5) +isin(27 × 5))
= 3^5 ( cos(135)+i sin(135))
= 3^5(-√2/2+i √2/2)
because : cos(135) = -√2/2 and sin(135) = √2/2
(3(cos27 +isin27)^5 = (- 3^5√2/2)+ i ( 3^5√2/2) ...(form : a+ib when
a= (- 3^5√2/2) and b = ( 3^5√2/2)

4 0

3 years ago

What is the common difference for the sequence shown below?

Alex Ar [27]

It is B because for every point going down, there is 3 to the left and so it is 1/3 and it has to be negative because its going left

4 0

2 years ago

Read 2 more answers

Russia has recently started a push for stronger smoking regulations much like those in western countries concerning cigarette ad

Blababa [14]

Answer:

a) 0.46

b) (2341.39, 3230.61)

c) For those Russians who do smoke, estimate the number of cigarettes smoked per day.= 23

Step-by-step explanation:

check below for more detailed solution

7 0

3 years ago

The owner of a clothing store borrows $5,000 for 1 year at 14.5% interest. If he pays the loan back at the end of the year, how

oksano4ka [1.4K]

Answer:

Depends on the sort of interest, He could have paid annual interest, compound interest, monthly. If it is annual interest the answer is 5,725$

Step-by-step explanation:

Multiply the initial value by the growth (1.145)

8 0

3 years ago

Are these triangles similar? if so, what postulate or theorem justifies that they are similar?

Karo-lina-s [1.5K]

Answer:

Yes The triangles are similar by SAS Similarity Theorem

Step-by-step explanation:

we know that

<u>Side-Angle-Side Similarity,</u> states that If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar

In this problem

Angle L is congruent with Angle Z

Verify if the included sides are proportional

$\frac{LJ}{ZY}=\frac{KL}{XZ}$

substitute the values

$\frac{3}{1.5}=\frac{4}{2}$

$2=2$ -----> is true

therefore

The triangles are similar by SAS

7 0

3 years ago

Simplify: log81/8 + 2log2/3 - 3log 3/2 +log 3/4​

Simplify: log81/8 + 2log2/3 - 3log 3/2 +log 3/4