The sum of two numbers is 82. The difference of the two numbers is 62. What are the two numbers?

Which table represents the graph of a logarithmic function in the form y=log3x when b>1?

alex41 [277]

Answer:

The satisfied table of the given function $y = log_{b} (x)$

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

Step-by-step explanation:

Explanation :-

Given logarithmic function $y = log_{b} (x)$ if b >1

Given first table

i)

put x = $\frac{1}{8}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{8} )$

$y = log_{2} (2^{-3} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3$

y = -3

ii)

put x = $\frac{1}{4}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{4} )$

$y = log_{2} (2^{-2} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2$

y = -2

iii)

put x = $\frac{1}{2}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{2} )$

$y = log_{2} (2^{-1} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1$

y = -1

iv)

put x = 1 given b > 1 so we can choose b = 2

$y = log_{2} (1 )$ = 0

y = 0

v)

put x = $2$ given b > 1 so we can choose b = 2

$y = log_{2} (2 )$

y = 1

Final answer:-

The satisfied table of the given function

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

8 0

3 years ago

Read 2 more answers

F(a)=a^4+3a^3-17a^2+2a-7 at a=3

Anon25 [30]

Answer:

a

Step-by-step explanation:

a

6 0

3 years ago

A catalog has a scale drawing of a floating dock. The dock is a regular octagon attached to a rectangular walkway. The scale dra

gtnhenbr [62]

Answer: 5 feet.

Step-by-step explanation:

Remember that the lenghts of the sides of a regular octagon are equal.

You can observe in the figure that the lenght of a side of the regular octagon is 1.25 inches.

Let be "s" the actual length of a side of the regular octagon.

Knowing that the scale drawing has a scale of 1 inch 4 feet, you can find the actual lenght of a side of this regular octagon with:

$s=\frac{(1.25in)(4ft)}{(1in)}\\\\s=5ft$

Therefore, the actual length of a side of the octagon is 5 feet.

6 0

2 years ago

What is the exact volume of the cone

Travka [436]

Answer:

V = $\frac{400}{3}$ $\pi$

Step-by-step explanation:

Volume of a cone is:

$V = \pi r^{2} \frac{h}{3}$

Substitute values given:

$V = \pi (5^{2} )(\frac{16}{3})$

$V = \pi (25)(\frac{16}{3} )$

V = $\pi \frac{400}{3}$

V = $\frac{400}{3}$ $\pi$

5 0

2 years ago

The half-life of cobalt-60 (used in

Likurg_2 [28]

Answer:

6.25 gm left

Step-by-step explanation:

Find the number of half lives in 26.3 years

26.3 / 5.26 = 5 half lives

(1/2) ^5 = 1/32 nd of the original will be left

1/32 * 200g = 6.25 gm left

5 0

2 years ago