Simplify into one logarithm 2 log x + 3 log y

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)

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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