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DiKsa [7]
3 years ago
15

Hi i need help with 15a(ii)

Mathematics
2 answers:
Ivahew [28]3 years ago
6 0

Answer:

5/2

Step-by-step explanation:

So first of all 1/log_3(4) can be written as log_4(3)...

So everything is base 4 except the log_8(x^3)...

We can play with this to get it so that the base is 4.

Let y=log_8(x^3) then 8^y=x^3

Rewrite 8 as 4^(3/2) so we have

4^(3/2 *y)=x^3

Now rewriting in log form gives: log_4(x^3)=3/2*y

Then solving that for y gives 2/3*log_4(x^3) or log_4(x^2)... let's put it back into the equation:

log_4(x^2+5x)-log_4(x^2)=log_4(3)

log_4((x^2+5x)/x^2)=log_4(3)

Set insides equal:

(x^2+5x)/x^2=3

Cross multiply:

x^2+5x=3x^2

Subtract 3x^2 on both sides:

-2x^2+5x=0

Factor

-x(2x-5)=0

So solutions are 0 and 5/2.  

We have to verify these...

0 isn't going to work because we can't do log of 0

it makes x^2+5x 0 and x^3 0

The only solution is 5/2.

Art [367]3 years ago
5 0

Answer:

x = 5/2

Step-by-step explanation:

log4(x^2+5x)-log8(x^3)=1/log3(4)

log(x^2 + 5 x) / log(4) - log(x^3) / log(8) = log(3) / log(4)

log(x (x+5))/log(4) - log(x^3) / log(8) = log(3) / log(4)

(3 log(x (x+5)) - 2 log(x^3)) / log(64) = log(3) / log(4)

3 log(x (x+5)) - 2 log(x^3) = 3 log(3)

log((3 x)/(x+5))=0

x=5/2

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the sum of three number number in an artithmetic product is 21. if second number isreduced by 1 and third term is increased by 1
grin007 [14]

The three numbers will be 12, 7, 2 and 3, 7, 11.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

Let the three consecutive numbers be a, a + d, and a + 2d

The sum of three numbers which are consecutive terms of an A.P. is 21.

a + a + d + a + 2d = 21

3(a + d) = 21

a = 7 - d

If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.

Then the number will be a, a + d − 1, a + 2d + 1. Then we have

\rm \dfrac{a + d - 1}{a} = \dfrac{a + 2d + 1}{a + d - 1}

On simplifying, we have

36 = a (8 + d)

a² - 15a + 36 = 0

On factorizing, the value of a will be

a² - 15a + 36 = 0

a² - 12a  - 3a + 36 = 0

(a - 12)(a - 3) = 0

a = 3, 12

If a = 12, then the value of d will be

d = 7 - 12

d = -5

If a = 3, then the value of d will be

d = 7 - 3

d = 4

Then the three numbers will be 12, 7, 2 and 3, 7, 11.

More about the sequence link is given below.

brainly.com/question/21961097

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7 0
2 years ago
executive committee consists of 15 ​members: 7 men and 8 women. 5 members are selected at random to attend a meeting in Hawaii.
larisa [96]

Answer:

1over3

Step-by-step explanation:

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7 0
3 years ago
Which of the following proportionally statements is correct?
yulyashka [42]

Answer:

\frac{AC}{BC}=\frac{DF}{EF}

Step-by-step explanation:

The figure given has two similar triangles: ΔABC and ΔDEF.  Although the triangles are similar, their orientation is different and ΔDEF is flipped.  Since the triangles are similar, their side lengths are proportional to each other.  Given the orientation of the triangles, we can still see that the diagonal (hypotenuse) for the larger triangle is AC and the smaller is DF.  The only answer that matches these up proportionally is the third one.  Looking at the second side, BC, we can see that this matches up to the longer leg of EF on the smaller triangle.  Final answer being:

\frac{AC}{BC}=\frac{DF}{EF}

6 0
3 years ago
If a car can go from 0 to 60 mi/hr in 8.0 seconds, what would be its<br> acceleration ?
tresset_1 [31]
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6 0
3 years ago
In the table below, x represents miles traveled and y represents the cost to travel by train.
Anastasy [175]

Answer:

The second equation is correct.

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Step-by-step explanation:

We can systematically eliminate the others.

For equation 3 and 4, 6.5*2 and 12*x is already bigger than 8 of the first set of numbers.

For equation 1, 2*x+8.5 is also bigger than 8 from the first set.

Plugging in the values to equation 2, we always get the correct cost.

5 0
3 years ago
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