All categories

3 years ago

Solve this equation 4log√x - log 3x =log x^2

Mathematics

1 answer:

ruslelena [56]3 years ago

5 0

Answer:

$x = \frac{1}{3}$

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒( $\frac{1}{3x}$ )

*rewrite to solve for x :

10⁰ = $\frac{1}{3x}$

1 = $\frac{1}{3x}$

1 · x = $\frac{1}{3x}$ · x

1x = $\frac{1}{3}$

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = $\frac{1}{3}$

You might be interested in

Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic O

oksano4ka [1.4K]

Answer:

a) Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

And the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And replacing we got:

$ME=1.96\frac{125}{\sqrt{16}}=61.25$

b) $ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =45 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

$n=(\frac{1.960(125)}{45})^2 =29.64 \approx 30$

So the answer for this case would be n=30 rounded up to the nearest integer

b. 30

c) And for this case the conditions in order to use the confidence interval are satisfied since:

a. Yes. The distribution of sample means is normal because the data are normal.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =125$ represent the population standard deviation

n=16 represent the sample size

Part a

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

And the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And replacing we got:

$ME=1.96\frac{125}{\sqrt{16}}=61.25$

c. 61.25 kg

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =45 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

$n=(\frac{1.960(125)}{45})^2 =29.64 \approx 30$

So the answer for this case would be n=30 rounded up to the nearest integer

b. 30

Part c

And for this case the conditions in order to use the confidence interval are satisfied since:

a. Yes. The distribution of sample means is normal because the data are normal.

7 0

3 years ago

Which statements about the value of the digits in the number 6,666,666 are true?

hammer [34]

I believe c and d are correct

5 0

3 years ago

Use the rectangle to answer the question.

nikitadnepr [17]

Answer:

12 x 9 = 108

Step-by-step explanation:

Just multiply the 2 given lengths when finding AREA of a rectangle.

7 0

3 years ago

Read 2 more answers

How many tenths are there in 4/5

Minchanka [31]

8 tenth because 4 over 5 is also 8 over 10

7 0

3 years ago

Read 2 more answers

This is just a question I want u guys to answer cause 99% of the adult population don't know the answer to this question.

Marrrta [24]

50/2 = 25

also can i have a brainliest

6 0

3 years ago

Solve this equation 4log√x - log 3x =log x^2​

Solve this equation 4log√x - log 3x =log x^2