All categories

2 years ago

What is log Subscript 15 Baseline 2 cubed rewritten using the power property?

Mathematics

2 answers:

nalin [4]2 years ago

7 0

Answer:

The equivalent expression

Step-by-step explanation:

Assuming your expression is $\log_{15}2^3$ , then we can use the power property of logarithm , which is $\log_ab^n=n\log_ab$ .

If we let a=15, b=2, and n=3

Then using the power property of logarithm will give us:

$\log_{15}2^3=3\log_{15}2$

Using the power property of logarithm, the equivalent expression is $3\log_{15}2$

garri49 [273]2 years ago

5 0

Answer:

Step-by-step explanation:

You might be interested in

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian

aev [14]

Answer: The answer is 11 (A)

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The variable complex number z is given by z=1+cos 2θ+isin2θ,where θ takes all values in the interval −1/2π<θ<1/2π

FinnZ [79.3K]

The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π

Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ

Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)

Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN

Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]
$\frac{1}{z} = \frac{(1+cos2\theta - i\, sin2\theta)}{(1 + cos 2\theta + i\, sin 2\theta)(1+cos2\theta - i \,sin2\theta)}\\ = \frac{1+cos2\theta - i \,sin 2\theta}{(1+cos2\theta)^{2} + sin^{2}2\theta}$

The denominator is
$(1+cos2\theta)^{2}+sin^{2}2\theta \\ = 1+2cos2\theta+cos^{2}2\theta+sin^{2}2\theta \\ =2cos2\theta+2 \\ = 2(1+cos2\theta)$

Therefore
$\frac{1}{z} = \frac{1}{2} -i \frac{sin2\theta}{2(1+cos2\theta)}$

The real part of 1/ = 1/ (constant).

6 0

2 years ago

W hich of these scales is equivalent to the scale 1 cm to 5 km? Select all that apply. (Lesson 1-11) A. 3 cm to 15 km D. 5 m

nordsb [41]

The equivalent scales are:

3 cm to 15 km is equivalent to 1 cm to 5 km ⇒ answer A

5 mm to 2.5 km is equivalent to 1 cm to 5 km ⇒ answer D

1 mm to 500 m is equivalent to 1 cm to 5 km ⇒ answer E

Step-by-step explanation:

To solve this problem do that

1. The given scale is 1 cm represents 5 km, then all given answer must

be change to cm and km

2. Find the equivalent scales to the given scale

∵ 3 cm represents 15 km

- Divide both of them by 3

∴ 1 cm represents 5 km

3 cm to 15 km is equivalent to 1 cm to 5 km

∵ 1 mm represents 150 km

- Change mm to cm

∵ 1 cm = 10 mm

∴ 1 mm = $\frac{1}{10}$ cm = 0.1 cm

∴ 0.1 cm represents 150 km

- Multiply both by 10

∴ 1 cm represents 1500 km

1 mm to 150 km is not equivalent to 1 cm to 5 km

∵ 5 cm represents 1 km

- Divide both my 5

∴ 1 cm represents 0.2 km

5 cm to 1 km is not equivalent to 1 cm to 5 km

∵ 5 mm represents 2.5 km

- Change mm to cm

∵ 1 cm = 10 mm

∴ 5 mm = $\frac{5}{10}$ cm = 0.5 cm

∴ 0.5 cm represents 2.5 km

- Divide both by 0.5

∴ 1 cm represents 5 km

5 mm to 2.5 km is equivalent to 1 cm to 5 km

∵ 1 mm represents 500 m

- Change mm to cm

∵ 1 cm = 10 mm

∴ 1 mm = $\frac{1}{10}$ cm = 0.1 cm

- Change m to km

∵ 1 km = 1000 m

∴ 1 m = $\frac{1}{1000}$ = 0.001 km

∴ 500 m = $\frac{500}{1000}$ = 0.5 km

∴ 0.1 cm represents 0.5 km

- Multiply both by 10

∴ 1 cm represents 5 km

1 mm to 500 m is equivalent to 1 cm to 5 km

Learn more:

You can learn more about the equivalent quantities in brainly.com/question/120752

#LearnwithBrainly

3 0

2 years ago

Find the value of x RT=4x+10 SW= 5x-20

Liula [17]

Well, as you can see from the rectangle RT and SW should have equal lengths. So to find the value of x, we need to do.....

4x + 10 = 5x - 20
-x + 10 = -20 (Subtraction property of equality)
-x = -30 (Subtraction property of equality)
x = 30 (Division property of equality)

To check our work:

4(30)+10 = 130
5(30)-20 = 130

So, the value of x is 30!

5 0

2 years ago

Rachel, Nancy, and Diego were in fishing competition. Rachel's fish was 7/8 foot long, Nancy's fish was 1/4 foot long, and Diego

Sidana [21]

It is 1/4 (.25), 1/2 (.5)and 7/8 (.875) from least to greatest

7 0

2 years ago