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3 years ago

The solution to the equation log2x + log2(x – 6) = 4 is x =

Mathematics

2 answers:

GenaCL600 [577]3 years ago

6 0

Answer:

Value of x=8

Step-by-step explanation:

Given : $log_2x+log_2(x-6)=4$

To find : The solution to the equation given

Solution :

Step 1- Write the given expression

$log_2x+log_2(x-6)=4$

Step 2 - Using logarithmic laws

$log_{b}x+log_by=log_bxy$

$log_2(x)(x-6)=4$

Step 3 - To remove log-base 2, we need to raise the left and right hand terms to power 2.

$(x)(x-6)=2^4$

$x^2-6x-16=0$

Step 4 - Solve the quadratic equation

$x^2-8x+2x-16=0$

$x(x-8)+2(x-8)=0$

$(x-8)(x+2)=0$

Either x=8 or x=-2

We neglect x=-2 because negative value is not defined in log.

Value of x=8

slava [35]3 years ago

3 0

Answer:

solution to the equation is 8

Step-by-step explanation:

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3 years ago

Help asap help please.

Xelga [282]

Answer:

30(x+1)/(x+7)

Step-by-step explanation:

This is not a rational expression because denominator has a domain of which it can be undefined.

To rationalize multiply by the reciprocal of the denominator (1/6+1/x+1)

___5___ *(6)(x+1) --> _____30(x+1)_____ --> 30x+1_ --> 30x+1

1/6+1/x+1 *(6)(x+1)--> 6(x+1)/6 + 6(x+1)/(x+1) --> (x+1)+6 --> x+7

Final Answer: 30(x+1)/(x+7)

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3 years ago

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velikii [3]

Answer:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .