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3 years ago

Solve for x. logx+log3=log18 Enter your answer in the box. x =

Mathematics

2 answers:

Murrr4er [49]3 years ago

7 0

Answer:

x=6

Step-by-step explanation:

We are given the equation here:

$logx+log3=log18$

Now we have log on both sides and we have to solve for x here.

At first let us bring log3 to the right side.

Here log3 is in addition on the right, so we will apply opposite operation of addition on the left. Opposite operation of addition is subtraction.

So subtracting log3 from right side, we have,

$logx=log18-log3$

Now we use division property of log,

$loga-logb=log\frac{a}{b}$

$logx=log\frac{18}{3}$

$logx=log6$

Now comparing both sides ,

x=6

marta [7]3 years ago

5 0

<u>Answer:</u>

x = 6.00001

<u>Step-by-step explanation:</u>

We are given the following log problem to solve for x:

log(x) + log(3) = log(18)

log(x) + 0.477121 = 1.255273

Adding -0.477121 to both the sides to get:

log(x) + 0.477121 + (−0.477121) = 1.255273 + (−0.477121)

log(x) + 0 = 0.778152

Dividing both the sides by 1 to get:

log(x) + 0/1 = 0.778152/1

log(x) = 0.778152

Solving the logarithm to get:

log(x) = 0.778152

10log(x) = 100.778152

x = 6.00001

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia

Arturiano [62]

Answer:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

$n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791$

So the answer for this case would be n=791 rounded up to the nearest integer

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)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$