Answer:
Step-by-step explanation:
<u>Given </u><u>:</u><u>-</u><u> </u>
And we need to find the potential solutions of it. The given equation is the logarithm of x² - 25 to the base e . e is Euler's Number here. So it can be written as ,
<u>Equation</u><u> </u><u>:</u><u>-</u><u> </u>
<u>In </u><u>general</u><u> </u><u>:</u><u>-</u><u> </u>
- If we have a logarithmic equation as ,
Then this can be written as ,
In a similar way we can write the given equation as ,
- Now also we know that
Therefore , the equation becomes ,
<u>Hence</u><u> the</u><u> </u><u>Solution</u><u> </u><u>of </u><u>the</u><u> given</u><u> equation</u><u> is</u><u> </u><u>±</u><u>√</u><u>2</u><u>6</u><u>.</u>
X=12.........................
Answer:
See below.
Step-by-step explanation:
There are a total of (75-3) / 3 + 1 = 25 numbers in the sequence. Now 24 of them can be paired so as to get a total of 81:
6 and 75, 9 and 72, 12 and 69............. 45 and 36, 42 + 39. That is 12 pairs with the number 3 the odd one out.
If we pick 15 random numbers there is no way we cannot pick one of these pairs which add up to 81. For example, if we pick 12 of the first numbers in the pairs and the number 3, there are 2 numbers left to pick and these 2 would be bound to match up with 2 of the numbers of the first 12.
If we pick only 6 of the first numbers in the pairs and the 3, there are another 8 numbers left to pick so at least 2 of these are bound to match up
with some of the the first 6. If we do not pick the 3 then at least 3 will match.
Whatever combination we pick will have 1 or more pairs which add up to 81.
