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3 years ago

Striped fNbric:

Mathematics

1 answer:

DIA [1.3K]3 years ago

4 0

Answer:

sssk

Step-by-step explanation:

sksks

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ln(y+1)-lny=1+3lnx . Express y in terms of x, in a form not involving logarithms. (4 marks, Maths CIE A level)

Delicious77 [7]

$remember$
$ln(x)=log_e(x)$
$and$
$log_x(a)-log_x(b)= log_x( \frac{a}{b} )$
$and$
$log_a(b)=c$ means $a^c=b$
$and$
$blog(a)=log(a^b)$

$so$

$ln(y+1)-ln(y)=1+3ln(x)$
$ln( \frac{y+1}{y} )=1+ln(x^3)$

$minus$ $ln(x^3)$ $from$ $both$ $sides$

$ln( \frac{y+1}{y}-ln(x^3) )=1$
$ln( \frac{y+1}{yx^3})=1$
$log_e( \frac{y+1}{yx^3})=1$

$translate$

$e^1=\frac{y+1}{yx^3}$
$e=\frac{y+1}{yx^3}$

$times$ $both$ $sides$ $by$ $yx^3$

$eyx^3=y+1$

$minus$ $y$ $from$ $both$ $sides$

$eyx^3-y=1$
$y(ex^3-1)=1$

$divide$ $both$ $sides$ $by$ $(ex³-1)$

$y= \frac{1}{ex^3-1}$

6 0

3 years ago

Read 2 more answers

All numbers less than 7 and greater than 7

mrs_skeptik [129]

Step-by-step explanation:

123456 less then 7

unlimited greater then 7

4 0

2 years ago

Which of the following is the inverse of y=3x?

shtirl [24]

Answer-

<em>The inverse of $y=3^x$ is </em>

$\boxed{\boxed{y=\log_3 x}}$

<u>Solution-</u>

The given function is,

$y=3^x$

We can get the inverse by interchanging he variable x and y among themselves and then separating each variables.

So in the inverse would be,

$\Rightarrow x=3^y$

Taking log of both sides,

$\Rightarrow \log x=\log 3^y$

As,

$\log a^b=b\times \log a$

Applying the same,

$\Rightarrow \log x=y\times \log 3$

$\Rightarrow y=\dfrac{\log x}{\log 3}$

As,

$\log_b a=\dfrac{\log a}{\log b}$

Applying the same,

$\Rightarrow y=\log_3 x$

Therefore, the inverse of $y=3^x$ is $y=\log_3 x$ .

7 0

3 years ago

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if y= 3x + 7 and the slope was multiplied by -1/2 would it become steeper become less steep or slope downward

amid [387]

By saying the slope was multiplied by -1/2, I assume you actually mean multiply and not decreased. In the equation, the slope of the equation is 3. Therefore, if it were to be multiplied by -1/2, the new slope would be -3/2. Because the slope is now negative, the slow would be downward. I hope this helps :-)

5 0

3 years ago

The HCF of two numbers is 6 and the product

nekit [7.7K]

Answer:

Step-by-step explanation:

There are two pairs of numbers whose product is 360, and their HCF is 6. They are 6 & 60, and 12 & 30.

4 0

2 years ago

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