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polet [3.4K]
3 years ago
14

28. Solve for x.

Mathematics
1 answer:
bija089 [108]3 years ago
5 0

Answer:

The value of x is 5 , - 5

Step-by-step explanation:

Given as :

Log_{2}(x + 3) + Log_{2}(x - 3) = 4

Now, <u>from log property</u>

Log_{b}m + [tex]Log_{b}n = [tex]Log_{b}(m × n)[tex]Log_{2}(x + 3) + Log_{2}(x - 3) = Log_{2}( (x + 3) × (x - 3) ) [tex]Log_{2}( (x + 3) × (x - 3) ) = 4Again  [tex]Log_{a}b = xSo , b = [tex]a^{x}

So,  (x + 3) × (x - 3) = 2^{4}

Or,  x² - 9 = 16

or,  x² = 25

∴  x = \sqrt{25}

I.e x = \pm 5

Hence the value of x is 5 , - 5  Answer

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Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of
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Answer:

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Step-by-step explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + <u>1</u>

3 = 2 + <u>1</u>

4 = 3 + <u>1</u>

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

sum =  \frac{n}{2} \{ a  + a  _{n}  \}

here,

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So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

S  =   \frac{25}{2}\{ 1  +25\}

=  \frac{25 \times 26}{2}

= 25  \times 13

= 325

So, the value of S comes out to be 325.

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