All categories

1 year ago

If log_10(x) = 3 + log_10(y), then find x/y

Mathematics

2 answers:

s344n2d4d5 [400]1 year ago

8 0

Answer:

x/y = 10^3 = 1000

Step-by-step explanation:

The rules of logarithms tell you ...

log(x/y) = log(x) -log(y)

Here, we have ...

log(x/y) = log(x) -log(y)

= (3 +log(y)) -log(y) = 3 . . . . . . . . substittute for log(x)

Taking the antilog, we get ...

log(x/y) = 3

x/y = 10^3 = 1000

_____

<em>Additional comment</em>

The expression log(x) is often used to refer to the "common log" of x, which is the logarithm to the base 10. This lets us avoid the cumbersome notation log_10(x).

In more formal mathematics, log(x) may be used to refer to the natural log. The distinction is usually made in high school algebra by referring to the natural log using ln(x).

Lina20 [59]1 year ago

7 0

Answer:

1000

Step-by-step explanation:

$log_{10}x = 3 + log_{10}y$
$log_{10}x - log_{10}y = 3$
$log_{10}(x/y) = 3$
$x/y = 10^3$
$x/y = 1000$

You might be interested in

Your payment is $375 per month for 36 months and you made a $2,500 a down payment

eimsori [14]

Answer:

$16,000?

Step-by-step explanation:

375 times 36 is 13500

Add 2500

and you have 1600

thats my guess

5 0

2 years ago

Read 2 more answers

Jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by

Elena-2011 [213]

The diagram of the lawn and the shed is shown below.

The area of the lawn needed to be mowed equals to the area of the yard minus the area of the shed

The area of the yard = $(5x)(13x-4) = 65 x^{2} -20x$
The area of the shed = $(2x)(2x+4)=4 x^{2} +8x$

The area of the lawn = $65 x^{2} -20x-(4 x^{2} +8x)$
The area of the lawn = $65 x^{2} -20x-4 x^{2} -8x$
The area of the lawn = $61 x^{2} -28x$

5 0

3 years ago

Look at the pic attached

Anni [7]

Answer:

x= -8 BDC= 68

EXPLANATION:

They create a straight angle which is always equal to 180. this means you must add both equations and set them equal to 180.

7 0

3 years ago

Can you help me with my maths?

Assoli18 [71]

Answer:

45. B, 9 + 0 = 9

46. D. 9 x 1 = 9

47. D. 0

48. B. 1/6 x 6 = 1

49. A

Step-by-step explanation:

3 0

3 years ago

Slope=-3 goes through (1,2) whats the equation

dedylja [7]

Hi student, let me help you out! :)

..............................................................................................................................................

We are asked to find the equation of the line, using the given information:

$\star~\mathrm{-3}$ , which is the slope

$\star~\mathrm{(1,2)}$ which is a point that the line contains

$\triangle~\fbox{\bf{KEY:}}$

The slope is the number before x, in the form $\mathtt{y=mx+b}$ .

Since "m" is the slope, and we're given what the slope is, we can substitute -3 for m:

$\dag~\mathtt{y=-3x+b}$

|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Now, we need to find the y intercept, "b", of the line.

Here's how it's done:

Remember the point that the line contains, (1,2)?

Well, its y-coordinate is 2; so what we do is substitute 2 for y:

$\dag~\mathtt{2=-3x+b}$