From 1st condition:

3^(x+1)=81
Take log on both sides,
➡ log [3^(x+1)]=log81
Use the property: log(x^a)=a logx
➡ (x+1) log 3=log(3⁴)
➡ (x+1) log 3=4×log 3
➡ (x+1)=4 (log 3 /log 3)
➡ x+1=4
➡ x=3➡↪➡↪ ANS

From 2nd condition, (Same process are repeated)

81^(x-y)=3
➡ 3^4(x-y)=3
➡ log [3^4(3-y)]=log 3
➡ 4(3-y) log 3=log 3
➡ (3-y)=(log 3)/(4log 3)
➡ 3-y=(1/4)
➡ y=11/4 ➡↪➡↪ ANS

4 0

3 years ago

Find an equation for the nth term of the arithmetic sequence. <br><br> -20, -16, -12, -8, .

quester [9]

A n =?
If the arithmetic sequence is:-20, - 16, - 12 , - 8 ...
a 1 = -20, d = 4 ( a 2 = -20 + 4 = -16, a 3 = -16+4 = -12,...)
And the formula for nth term is:
a n = a 1 + d (n -1)
a n = -20 + 4( n -1) (n=1.2.3...)

8 0

3 years ago

A stick is broken at a point, chosen at random, along its length. Find the probability that the ratio, R, of the length of the s

Oksanka [162]

Solution :

Let the distance of the stick from one break be X

And let us assume that $X \leq l/2$ .

Here, l = length of stick

Therefore, $$P(X$

We know that, $R=\frac{X}{l-X}$ , so by definition we get

$X =\frac{lR}{1+R}$

The cumulative distribution function for R is

$$P(R$

When it starts at zero, then r =0. It ends at one when the r has a maximum

value of one.

The probability density function is given by

$\frac{d}{dr}(\frac{2r}{1+r})= \frac{2}{(r+1)^2}$

Now integrating, we find E(R) and $E(R)^2$ gives :

$E(R) =\int\limits^1_0 \frac{2r}{(1+r)^2} \, dr = 2 \ln 2-1$

$E(R)^2= 3 - 4\ln 2$

Therefore, Var(R)= $2-4(\ln \ 2)^2$

3 0

3 years ago

PLEASE HELP ME FAST!! IT'S URGENT!!

juin [17]

Steve didn't put the parenthesis when he went to the second part of the equation, instead of putting the parenthesis he skipped them and keep going along with the equation.

I don't know if you needed this but the answer to the math problem would be

Answer: 2 x

3 0

3 years ago