Question

please explain how solve this question.
( {EXPLAIN} )​

Answer 1

x = 3/5

Step-by-step explanation:

Given :-

2^7x / 2^2x = 5th root of 2^15

To find :-

Find the value of x ?

Solution :-

Given that:

2^7x / 2^2x = 5th root of 2^15

We know that

a^m / a^n = a^(m-n)

Where a = 2 , m = 7x and n = 2x

On applying this formula then

=> (2)^(7x-2x) = 5th root of 2^15

=> 2^5x = 5th root of 2^15

We know that

nth root a = a^1/n

=> 2^5x = (2^15)^1/5

We know that

(a^m)^n = a^mn

=> 2^5x = 2^(15/5)

=> 2^5x = 2^3

If bases are equal then exponents must be equal

=> 5x = 3

=> x = 3/5

Therefore, x= 3/5

Answer:-

The value of x for the given problem is 3/5

Check:-

If x = 3/5 then

LHS = 2^7x / 2^2x

=> 2^7(3/5) / 2^2(3/5)

=> 2^(21/5) / 2^(6/5)

=> 2^[(21/5)-(6/5)]

=> 2^(21-6)/5

=> 2^(15/5)

=> 2^3

=> 2×2×2

=> 8

RHS = 5th root of 2^15

=> (2^15)^1/5

=> 2^(15/5)

=> 2^3

=> 2×2×2

=> 8

LHS = RHS is true for x = 3/5

Used formulae:-

• a^m / a^n = a^(m-n)

• nth root a = a^1/n

• (a^m)^n = a^mn

Answer 2

Answer:

$\frac{ {2}^{7x} }{ {2}^{2x} } = \sqrt[5]{ {2}^{15} } \\ \\ = {2}^{7x - 2x} = {2}^{ \frac{15}{5} } \\ \\ = {2}^{5x} = {2}^{3} \\ \\ = > 5x = 3 \\ = > x = \frac{3}{5}$