Question

find the value of n​

Answer 1

Answer:

Heres your answer mate :

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Answer 2

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GIVEN :

${7}^{2n + 1} \div 49 = {7}^{3}$

Required to Find :

1. Value of n

Solution :

In the question we were asked to find the value of "n"

so,

To find the value of n we need to use the basic laws of exponents.

I think you may be wondering what are laws of exponents.

Laws of exponents are nothing but some simple type of formulas used in solving questions.

So,

Here I want to give some laws of the exponents which is used in the above sum.

$1. \: \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$2. \: \: \: \frac{1}{ {a}^{ n} } = \: {a}^{ - n}$

(This is read as a power m multipled with a power n is equal to a power m plus n )

so, let's coming to the sum

using the above law of the exponent

we get,

${7}^{2n + 1} \div 49 = {7}^{3} \\ {7}^{2n + 1} \div {7}^{2} = {7}^{3} \\ {7}^{2n + 1} \times \frac{1}{ {7}^{2} } = {7}^{3} \\ {7}^{2n + 1} \times {7}^{ - 2} = {7}^{3} \\ {7}^{2n + 1 - 2} = {7}^{3}$

If bases are equal powers are also equal.

so equal the powers on both sides

we get,

2n + 1 - 2 = 3

2n - 1 = 3

2n = 3+1

2n = 4

n = 4/2

n = 2

Therefore,

value of n is 2