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nexus9112 [7]
3 years ago
9

What is the solution to log (9x)-log 3 = 3?

Mathematics
1 answer:
xeze [42]3 years ago
5 0

Answer:

The solution x = \frac{e^{3} }{3}

Step-by-step explanation:

<u>Step 1</u>:-

Given log(9 x) -log 3 =3

we have to use formula  log a-log b=log\frac{a}{b}

log(9 x)- log 3 = log(\frac{9 x}{3} ) =3

Again by using formula log a =b

                                       a = e^{b}

so \frac{9 x}{3} =e^{3}

<u>step 2:</u>-

   3 x = e^{3}

  x = \frac{e^{3} }{3}

The solution of given problem is x=\frac{e^3}{3}

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2. Which of the following systems of inequalities represents the graph?
Rom4ik [11]

Answer:

Option: D is the correct answer.

D)  –2x + y ≥ 4

         x + y < 2

Step-by-step explanation:

We are asked to find the linear inequality that represents the following graph.

Clearly from the graph we could observe that one line is dotted and the other is solid line.

i.e. one inequality is strict while the other is a inequality with equality sign.

<u>Dashed line:</u>

It passes through (0,2) and  (2,0).

Hence, the equation of line is:

y-2=\dfrac{0-2}{2-0}\times (x-0)\\\\\y-2=\dfrac{-2}{2}\times x\\\\y-2=-x\\\\x+y=2

As the shaded region is towards the origin.

Hence, the inequality will be:

x+y<2.

<u>Solid line:</u>

The line passes through (-2,0) and (0,4).

hence equation of line is:

y-0=\dfrac{4-0}{0-(-2)}\times (x+2)\\\\

i.e

y=\dfrac{4}{2}\times (x+2)\\\\y=2\times (x+2)\\\\y=2x+4\\\\-2x+y=4

Now, as the shaded region is away from the origin hence the inequality which will be used is:

-2x+y\geq 4

Hence, option: D is the correct answer.

D.   –2x + y ≥ 4

       x + y < 2

8 0
3 years ago
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To convert hour into minute: (No. of hour × 60) minutes

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2 years ago
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Ryan surveyed parents. He found 3 out of every 5 parents vote. 450 parents eligible. How many parents will vote in the election?
Dafna1 [17]
The answer is 150 parents. Because 450/3=150
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3 years ago
Every integer number is also a. Irrational number b. Whole number c. Natural number d. Rational number
const2013 [10]

Answer:

Option d

Step-by-step explanation:

Other options are not eligible because

a) Integers are not irrational

b)Whole numbers start from 0 and consists positive integers only.But integers consist negative integers also.

c)Natural number consists of positive integers only.

If the question had been asked as some integers are also, then options b) and c) could have been written . But in this case , it is asked every integer is also.

Thank you!

5 0
2 years ago
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ExtremeBDS [4]

Answer:

Step-by-step explanation:

hello : write this expression

X² + y² + 6x – 2y+3 = 0  in the standard form

(x²+6x) +(y²-2y) +3 = 0

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but : 7 = (√7)²

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