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3 years ago

Write the expression as a single logarithm

Mathematics

1 answer:

klio [65]3 years ago

4 0

1/2 [3logx + logy]

Step 1:

we use the property of n logx =log xⁿ for 3 logx

so 1/2[3logx +logy]= 1/2 [log x³ + log y]

Step 2:

We use another property here log a + log b = log (ab)

1/2[log x³y]

Step 3:

we again use the property of n logx =log xⁿ, bringing 1/2 in power

[log x³y]^1/2

√log(x³y)

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What is 3/5th of 42,000

Kipish [7]

We set up a proportion: ?/42,000= 3/5

Cross multiply:
5*?= 3*42,000
⇒ ?= 3*42,000/5= 25,200

3/5 of 42,000 is 25,200~

7 0

4 years ago

Which value of x from the set {4, 5, 6, 7}, makes this equation true? 4(8 − x) = 8

vekshin1

4(8 - x) = 8, 32 - 4x = 8, -4x = -24, So x = 6

8 0

3 years ago

Read 2 more answers

Aaron and noah wanted to have a contest to see which of their paper airplanes could fly the longest distance. Aaron's plane flew

Marina CMI [18]

Aaron's plane flew 3.21 meters further than Noah's plane.

Explanation

Aaron's plane flew 4 meters and Noah's plane flew 79 centimeters.

So, first we need to convert 79 centimeters into meters.

We know that, 1 centimeter = 0.01 meter

So, 79 centimeters = $(0.01*79)meter= 0.79 meter$

Now, the difference of distance between Aaron's plane and Noah's plane is $(4-0.79) meters = 3.21 meters$

3 0

4 years ago

4. Find the value of x in the right triangle below. 60°

antiseptic1488 [7]

Answer:

Step-by-step explanation:

It is worthwhile memorizing the ratios of legs in a 30°–60°–90° triangle. Shortest to longest, the ratios are ...

1 : √3 : 2

Then the sides marked will have the ratio ...

6 : x = 1 : 2 = 6 : 12

x = 12

_____

You can also get there using trigonometry.

cos(60°) = 6/x

x = 60/cos(60° = 60/0.5

x = 12

7 0

3 years ago

Given equation x = 6 + i, w = -1 + 5i and z = 4 - 8i, determine each of the following in the form of a + bi

Temka [501]

Answer:

i) 28 - 30i

ii) 36 + 28i

Step-by-step explanation:

i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i

z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i

2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i

ii) w = -1 + 5i and z = 4 - 8i

w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40 $i^{2}$ ⇒collect like terms

w × z = -4 + 28i - 40 $i^{2}$

∵ $i^{2}=-1$

∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i

3 0

3 years ago