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2 years ago

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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Decompose 4/6 into three fractions with three different numerators

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2/3 6/9 9/12 are three fractions with different numerator

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3 years ago

Suppose that the proportions of blood phenotypes in a particular population are as follows: A B AB O 0.48 0.13 0.03 0.36 Assumin

Serggg [28]

Answer:

P(O and O) =0.1296

P=0.3778

Step-by-step explanation:

Given that

blood phenotypes in a particular population

A=0.48

B=0.13

AB=0.03

O=0.36

As we know that when A and B both are independent that

P(A and B)= P(A) X P(B)

The probability that both phenotypes O are in independent:

P(O and O)= P(O) X P(O)

P(O and O)= 0.36 X 0.36 =0.1296

P(O and O) =0.1296

The probability that the phenotypes of two randomly selected individuals match:

Here four case are possible

P=P(A and A)+P(B and B)+P(AB and AB)+P(O and O)

P=0.48 x 0.48 + 0.13 x 0.13 + 0.03 x 0.03 + 0.36 x 0.36

P=0.3778

7 0

3 years ago

Workers on the assembly line produce 4x + 6 boats each day. Which expression shows how many boats they produced in 12 days?

Annette [7]

We're going to assume that x = # of days.
Plug 12 in as x:
4 × 12 = 48
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7 0

3 years ago

Read 2 more answers

In the transformation ABC A'B'C', the preimage of B' is ____. . a0

Misha Larkins [42]

Answer:

Pre image of B' is B

Step-by-step explanation:

Given:

ABC is a triangle

A transformation is done on ABC so that the image is A'B'C'.

Note that transformations are of various types such as dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.

In any type of transformation, corresponding vertices will be matched. In other words, A will become A', B will become B' and C will become C'.

Because of the property of the transformation to keep images similar and also transforming correspondingly the vertices we get preimage of B' would be nothing but B itself.

8 0

3 years ago

HEEELP

Drupady [299]

Answer: (c)

Step-by-step explanation:

Given

$f(x)=\dfrac{1}{x-3}\\\\g(x)=\sqrt{x+5}$

Here, $\sqrt{x+5}\ \text{is always greater than equal to 0}\\\Rightarrow x+5\geq 0\\\Rightarrow x\geq -5\quad \ldots(i)$

To get $f\left(g(x)\right)$ , replace $x$ in $f(x)$ by $g(x)\ \text{i.e. by}\ \sqrt{x+5}$

$\Rightarrow f\left(g(x)\right)=\dfrac{1}{\sqrt{x+5}-3}\\\\\text{Denominator must not be equal to 0}\\\\\therefore \sqrt{x+5}-3\neq0\\\Rightarrow \sqrt{x+5}\neq 3\\\Rightarrow x+5\neq 9\\\Rightarrow x\neq 4\quad \ldots(ii)$

Using $(i)$ and $(ii)$ it can be concluded that the domain of $f\left(g(x)\right)$ is all real numbers except 0.

Therefore, its domain is given by

$x\in [-5,4)\cup (4,\infty)$

Option (c) is correct.

5 0

3 years ago