Question

If 3 raised to the power of x is equal to 900 then find the value of 3^x+2 minus3^x-2

Answer 1

Given that,

${3}^{x} = 900$
We have to find the value of,

${3}^{x + 2} - {3}^{x - 2}$
We know that is exponents are added this means they are multiplied with the powers of same base
That is,
${a}^{x + y} = {a}^{x} \times {a}^{y}$
So,
${3}^{x + 2} = {3}^{x} \times {3}^{2}$

and is exponents are subtracted this means they are divide by the powers of same base

That is,
${a}^{x - y} = {a}^{x} \div {a}^{y}$
So

${3}^{x - 2} = {3}^{x} \div {3}^{2}$

Now,
${3}^{x + 2} - {3}^{x - 2} \\ \\ = > {3}^{x} \times {3}^{2} - {3}^{x} \div {3}^{2}$
Given that 3^x = 900

So substitute the value of 3^x

$= > 900 \times {3}^{2} - 900 \div {3}^{2} \\ \\ = > 900 \times 9 - 900 \div 9 \\ \\ = > 8100 - 100 \\ \\ = > 8000$

So your answer is 8000


Hope it helps dear friend ☺️

Answer 2

8000 is the answer of the question