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OLEGan [10]
3 years ago
13

Simplify into one logarithm 2 log x + 3 log y

Mathematics
1 answer:
const2013 [10]3 years ago
8 0
If a logarithm has a coefficient, then the coefficient can also be written as the exponent of the input of the logarithm. In other words, if you have the logarithm alog(x), that is equal to log(x^a). So the expression can be rewritten:

log(x^2)+log(y^3)

If tow logarithms of the same bases are added together that is equal to the logarithm of the product of the inputs of the two original logarithms. In other words, given log(x)+log(y), it can also be written as log(xy). So the expression can be combined into one logarithm:

log(x^2 * y^3)
You might be interested in
Does the system have no solution?​
kvv77 [185]

Answer:

\mathrm{A)\:}-6

Step-by-step explanation:

Notice that in the second equation, the coefficient of y is 2 times greater than in the first. Therefore, by making the coefficient of x in the second equation 2 times greater than in the first, it's impossible to only isolate one variable.

Therefore, when a=-3\cdot 2=\fbox{-6}, there are no solutions to this system.

6 0
3 years ago
A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let
kozerog [31]

Answer:

b. A binomial variable with 25 independent trials

Step-by-step explanation:

The conducted experiment is binomial experiment because outcome can be divided into success or failure. The success would be the people who read novel in the past year and also responses are independent of each other. We have to find the number of trials n in the given problem.

we are given that variance of R=6 and p=probability of success=0.4.

We know that variance of binomial distribution is

Variance=npq

where q=1-p=1-0.4=0.6.

By putting the values in variance formula, we can get the value of n.

6=n*0.4*0.6

6=0.24*n

n=6/0.24

n=25

Hence, random variable R is a binomial variable with 25 independent trials.

4 0
2 years ago
A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (–3, 1), (1, 1), and (1, –2). What
vladimir2022 [97]

Answer:

The perimeter of the triangle is 12\ units

Step-by-step explanation:

Let

A(-3,1),B(1,1),C(1,-2)

we know that

The perimeter of triangle is equal to

P=AB+BC+AC

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance AB

A(-3,1),B(1,1)

substitute in the formula

AB=\sqrt{(1-1)^{2}+(1+3)^{2}}

AB=\sqrt{(0)^{2}+(4)^{2}}

AB=4\ units

step 2

Find the distance BC

B(1,1),C(1,-2)

substitute in the formula

BC=\sqrt{(-2-1)^{2}+(1-1)^{2}}

BC=\sqrt{(-3)^{2}+(0)^{2}}

BC=3\ units

step 3

Find the distance AC

A(-3,1),C(1,-2)

substitute in the formula

AC=\sqrt{(-2-1)^{2}+(1+3)^{2}}

AC=\sqrt{(-3)^{2}+(4)^{2}}

AC=5\ units

step 4

Find the perimeter

P=AB+BC+AC

substitute the values

P=4+3+5=12\ units

6 0
3 years ago
A series of quarterly payments of P1,300 each at the first payment is due at 4 years, and the last payment at the end of 12 year
gtnhenbr [62]

Answer:

The Value of Payments is  P18,557.15

Step-by-step explanation:

The quarterly payment is an annuity payment.

Use the following formula to calculate the present value of the payments.

PV of Annuity = Annuity Payment x ( 1 - ( 1 + interest rate )^-Numbers of periods ) / Interest rates

Where

Annuity Payment = Quarterly payment = P1,300

Interest rate = 5.12% x 3/12 = 1.375%

Numbers of periods = 4 years x 12/3 = 16 quarters

PV of Annuity = Value of Payments  = ?

Placing values in the formula

Value of Payments = P1,300 x ( 1 - ( 1 + 1.375% )^-16 ) / 1.375%

Value of Payments =  P18,557.15

4 0
2 years ago
Tamara is going to the laundromat. She needs 6 quarters for each of the 4 machines that she is using. How many dollar bills must
jekas [21]
6 x 4 = 24

24 / 4 (#ofquartersinadollar) = 6
It’s option D.
5 0
3 years ago
Read 2 more answers
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