# MATH Archive

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## Properties of Logs

1. Evaluate each of the following expressions using the propeties of logs (and no calculator)

$log_{3}\sqrt[3]{81}=log_{3}\left&space;(&space;81&space;\right&space;)^{\frac{1}{3}}=log_{3}\left&space;(&space;3^{4}&space;\right&space;)^{\frac{1}{3}}=log_{3}3^{\frac{4}{3}}=\frac{4}{3}\cdot&space;log_{3}3=\frac{4}{3}$ Read the rest of this entry »

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## Për ERLËN

Try to understand the exercise by pictures.Write the inequality as a system.  Read the rest of this entry »

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## How many numbers has 2 to the 100th?

How many numbers has $2^{100}$?

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## The sum of n first numbers of the string 7,77,777,….

Find the sum of  n first numbers of the string  7,77,777,…. Read the rest of this entry »

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## Compare two functions.

For the given functions $f:y=\frac{2x^{2}+5x+3}{2x+1}$  and  $g:y=5x$ . a)Show that in [1;+∞[ , f(x)≤g(x).

To compare two functions,make their difference.

$f(x)-g(x)=\frac{2x^{2}+5x+3}{2x+1}-5x=\frac{2x^{2}+5x+3-5x(2x+1)}{2x+1}=\frac{2x^{2}+5x+3-10x^{2}-5x}{2x+1}=\frac{-8x^{2}+3}{2x+1}<0$ for  x≥1.

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## Solve the equation.

Solve the equation
$\left&space;(&space;x+1&space;\right&space;)^{4}+x^{4}=17$

Write  x+1=t Read the rest of this entry »

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## Quiz. Trigonometry.

1-In the statements below find which is True and which is False Read the rest of this entry »

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## Geometric progression-Exercise

Exercise 1

In a square that has side a, by bringing together the middle of the sides,is formed a new square.In the new square ,in the same way,is formed another new square,and by the same wasy another one… infinity

a)      Show that the string of perimetres of the squares is infinite decreasing geometric progression.

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## Geometric Progression-Exercise 2

The sum of the numbers of an infinite decreasing geometric progression is 8. Find y1 dhe q, considering that the sum of their cubes is $\frac{512}{7}$. Read the rest of this entry »

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## Function and numerical sequence

1Find the domain of the function: Read the rest of this entry »