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djyliett [7]
2 years ago
15

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

Mathematics
2 answers:
s344n2d4d5 [400]2 years 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]2 years 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

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Segment AB has endpoints on the coordinate grid where A is (- 18, 5) and B is (- 4, 5) Point Z is located exactly 1/8 of the dis
fenix001 [56]

Given:

Endpoints of segment AB are A(- 18, 5) and B(- 4, 5).

Point Z is located exactly 1/8 of the distance from A to B.

To find:

The value of the x-coordinate of point Z.

Solution:

Point Z is located exactly 1/8 of the distance from A to B.

AZ:AB=1:8

AZ:ZB = AZ:(AB-AZ)= 1:(8-1) = 1:7

It means point Z divided segment AB in 1:7.

Using section formula, the x coordinate of point Z is

x-coordinate=\dfrac{mx_2+nx_1}{m+n}

x-coordinate=\dfrac{1(-4)+7(-18)}{1+7}

x-coordinate=\dfrac{-4-126}{8}

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x-coordinate=-16.25

Therefore, the required x-coordinate of point Z is -16.25.

3 0
3 years ago
An equation is shown below: 3(4x − 2) = 1 Which of the following correctly shows the first two steps to solve this equation?
Svetlanka [38]

Answer:

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3 years ago
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In 2018, the number of students at The Villages High School was 975 and is increasing at a rate of 2.5% per year. Write and use
avanturin [10]

Answer:

A(t)=975(1.025)^t

In 2025,the number of students at the villages high school=1159

Step-by-step explanation:

We are given that in 2018

Number of students at the villages high school=975

Increasing rate,r=2.5%=0.025

We have to write and use of exponential growth function to project the populating in 2025.

A_0=975,t=0

According to question

Number of students at the villages high School is given by

A(t)=A_0(1+r)^t

Substitute the values

A(t)=975(1+0.025)^t=975(1.025)^t

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2 years ago
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Answer:

The top option is false.

Step-by-step explanation:

Both segments have a <em>rate</em><em> </em><em>of</em><em> </em><em>change</em><em> </em>[<em>slope</em>] of ⅔. It just that their ratios have unique qualities:

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<em>BC</em><em> </em>is at a 4⁄6 slope, and <em>AB</em><em> </em>is at a ⅔ slope. Although their quantities are unique, they have the exact same value.

I am joyous to assist you anytime.

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