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2 years ago

O log2 3x + log2 3=2

Mathematics

1 answer:

ipn [44]2 years ago

8 0

Answer:

$\large\boxed{x=\dfrac{4}{9}}$

Step-by-step explanation:

$\log_23x+\log_23=2\\\\\bold{DOMAIN}:\\3x>0\to x>0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_2\bigg[(3x)(3)\bigg]=2\\\\\log_29x=2\qquad\text{use}\ \log_ab=c\iff a^c=b\\\\\log_29x=\log_22^2\\\\\log_29x=\log_24\iff9x=4\qquad\text{divide both sides by 9}\\\\\dfrac{9x}{9}=\dfrac{4}{9}\\\\\boxed{x=\dfrac{4}{9}}\in \bold{DOMAIN}$

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Sam needs a web designer. Designer A is offering her services for an initial $500 in addition to $100 per hour. Designer B is of

gavmur [86]

Answer:

2 hours

Step-by-step explanation:

Let's denote the amount of time we need to find out, t.

=> 600 + 50t < 500 + 100t

or 600 - 500 < 100t - 50t

or 100 < 50t

or 100/50 < t

or t > 2

=> After 2 hours, company B will be cheaper option than company A

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2 years ago

The hypotenuse of a right triangle is 50 millimeters long. One leg of the right triangle is 30 millimeters long. What is the len

alexandr1967 [171]

First. we use the Pythagorean theorem:
$a {}^{2} + b {}^{2} = c {}^{2}$
Add the numbers in
${30}^{2} + {b}^{2} = {50}^{2}$
start simplifying
${b}^{2} = 1600$
$b = 40$

So, the leg has a length of 40 mm.

6 0

3 years ago

Please I need your help

Svetllana [295]

Answer:

249mm

Step-by-step explanation:

You find volume of the overall figure- 11 x 3 x 13= 429

Then find volumes of missing parts of overall complete figure and subtract from the overall volume....

5 x 4 x 3= 60

429-60=369

-------------------------------------

8 x 5 x 3= 120

369-120= 249

Hope this helped!! Hope you got it- please leave a rating and mark as Brainliest. Thank You :) (I really want to go to sleep right now, would have explained further, sorry)

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3 years ago

What is 50 minutes as a fraction of 1 hour 15 minutes

TiliK225 [7]

Answer:

Step-by-step explanation:

15 minutes of an hour is 15/60. So 15/60 can be simplified to 1/4.

4 0

1 year ago

Karen works 42 hours in a week and earns 6.85 per hour. Estimate the amount of money she earns in a week.

katen-ka-za [31]

Answer:

287.7 u gotta be kidding,

Step-by-step explanation:

42×6.85=287.7

7 0

2 years ago

Read 2 more answers