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Log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)​

Answers

Answer 1
Answer:

I assume you're referring to the product,

\log_(5t)(5t+1)\cdot\log_(5t+1)(5t+2)\cdot\cdots\cdot\log_(5t+n)(5t+n+1)

Recall the change-of-base identity:

\log_ab=(\log_cb)/(\log_ca)

where c > 0 and c ≠ 1. This means the product is equivalent to

(\log(5t+1))/(\log(5t))\cdot(\log(5t+2))/(\log(5t+1))\cdot\cdots\cdot(\log(5t+n+1))/(\log(5t+n))

and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to

(\log(5t+n+1))/(\log(5t))=\boxed{\log_(5t)(5t+n+1)}

Related Questions

1) If a bookshelf is 28 inches long, how many 1 inch books will fit on the bookshelf?​
Does the graph below represent a function? A. YesB. NoC. SometimesD. Not enough information.
Factor 6(2p q)^2 -5(2p q) - 25
A total of 30 tomato plants were grown in a greenhouse under various conditions consisting of combinations of soil type (I, II, III, IV, and V), and fertilizer type (A,B,C). There were an equal number of plants grown under each combination. After a fixed period of time, the yield (in kilograms) of tomatoes from each plant was measured. What type of experimental design is this?
Can someone plzzz help me

at the same time a 15 foot pole casts a 7.5 foot shadow a nearby tree casts an 11 foot shadow how tall is the tree​

Answers

answer: 22

15/7.5 = x/11

cross multiply

7.5x = 165

divide by 7.5 on both sides to get the x alone

7.5x/7.5 = 165/7.5

x = 22

the tree is 22 feet

sorry if it’s wrong

Question 3 (1 point)What is the value of x in the equation 8+4 = 2(x - 1)?
a
11/2
b
13/2
c
5
d
7

Answers

Answer:

D. 7

Step-by-step explanation:

(8+4) = 2(x-1) multiply (x-1) by 2

(8+4) = 2x-2 add 8 and 4

12 = 2x-2 add 2 on both sides

14 = 2x divide both sides by 2

7 = x

Answer is D

12 = 2x - 2

14 = 2x

14/2 = x

7 = x

If BC = x − 2, CD = 19, and BD = 3x − 11, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type the answer in a step by step.

Answers

Answer:

UV = 15

BD= 31

Step-by-step explanation:

Since, U is the midpoint of TV.

Therefore,

TU = UV

x + 10 = 3x

x - 3x = - 10

-2x = - 10

x = - 10/-2

x = 5

UV = 3x = 3*5

UV = 15

BD = BC + CD

3x - 11 = x - 2 + 19

3x - 11 = x + 17

3x - x = 11 + 17

2x = 28

x = 28/2

x = 14

BD = 3x - 11 = 3*14-11 = 42 - 11

BD= 31

Final answer:

We used the relationship that BC + CD = BD and then solved for x, which we found to be 14. We then substituted 14 for x in the equation for BD, which gave us a result of 31.

Explanation:

In the given question, we have a piece of a line divided into different sections: BC, BD, and CD with their respective lengths. BD is represented through a variable equation. We know that BC + CD = BD, this is a fundamental property of geometry that the sum of the lengths of two consecutive sections of a line is equal to the total length. So, substitute the given values:

x − 2 + 19 = 3x − 11

Simplify the equation by combining like terms: x + 17 = 3x - 11. Now, let's solve for x:

First, consolidate x's on one side by subtracting 'x' on both sides. We get 17 = 2x - 11.

Next, add 11 on both sides to solve for x. We get, 28 = 2x.

Finally, divide by 2 on both sides to find x, x = 14.

Now, we can find BD by substituting x into the equation 3x - 11, we get:

BD = 3*14 - 11 = 42 - 11 = 31.

Learn more about Algebraic Equations here:

brainly.com/question/31303181

#SPJ2

Problem 9-10 The elongation of a steel bar under a particular tensile load may be assumed to be normally distributed, with a mean of .06 in. and standard deviation of .008 in. A sample of n=100 bars is subjected to the test. Find the probability that the sample mean elongation is between .0585 in. and .0605 in.

Answers

Answer:

The answer is 0.7036.

Step-by-step explanation:

Check the attached file for the computations.

The probability that the mean life of a random sample mean elongation is between .0585 in. and .0605 in. is 70.57%

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean.

It is given by:

z = (raw score - mean) / (standard deviation÷√sample)

Mean = 0.06, standard deviation = 0.008, sample = 100.

For x = 0.0585:

z = (0.0585 - 0.06)/ (0.008 ÷√100) = -1.88

For x = 7.2:

z = (0.0605 - 0.06)/ (0.008 ÷√100) = 0.623

P(-1.88 < z < 0.63) = P(z < 0.63) - P(z < -1.88) = 0.7357 - 0.03 = 0.7057

The probability that the mean life of a random sample mean elongation is between .0585 in. and .0605 in. is 70.57%

Find out more on z score at: brainly.com/question/25638875

Data Entry - No Scoring During your procedure to determine the uncalibrated volume near the stopcock of your buret, what was the mass in grams of water that drained out when the meniscus started just above the 25 mL mark and ended just above the stopcock? Report to the thousandth of a gram.

Answers

Answer:

0.025 grams

Step-by-step explanation:

The water in the stopcock has a volume of 25 mL initially, After that, the whole water was drained out. So we have:

Volume of drained water = (25 mL)(1 x 10⁻⁶ m³/1 mL)

Volume of drained water = 25 x 10⁻⁶ m³

Density of drained water = 1000 kg/m³

So, for the mass of drained water:

Density of drained water = Mass of drained water/Volume of drained water

Mass of drained water = (Density of drained water)(Volume of drained water)

Mass of drained water = (1000 kg/m³)(25 x 10⁻⁶ m³)

Mass of drained water = 0.025 gram

Density

F(x) =x2 + x + 1
6(x-4)
SERE
g(x) = x2+x+1
8(x-4)
Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?
The oblique asymptote for g(x) is steeper than for f(x).
Both functions have the same oblique asymptote.
The oblique asymptote for f(x) is steeper than for g(x).
Both functions have parallel oblique asymptotes.

Answers

Answer:

The oblique asymptote fo f(x) is steeper than for g(x).

Step-by-step explanation:

Just took the test and got it right

Answer:

The answer is c

Step-by-step explanation:
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