Question

find the value of x if 2^( 7x )÷2^( 2x ) = √2^( 15)

Answer 1

2^7x-2x=2^15/2
2^5x=2^15/2

equating powers of same bases

5x=15/2
x=15/10
x=3/2

Answer 2

Concept

Equation in single variable which can be solved to find value of the variable.

Given

$2^{7x}$ / $2^{2x}$ = $2^{15/2}$

Find

The value of x which satisfies the above equation.

Solution

As we know according to exponential property,  $x^{a} /x^{b} = x^{a-b}$ ,

The given equation can be rewritten as  $2^{7x-2x} = 2^{15/2}$ ,

$2^{5x} = 2^{15/2}$

now equating the powers of both sides ,

5x=15/2

x=3/2

The value of x which satisfies the given equation $2^{7x}$ / $2^{2x}$ = $2^{15/2}$ is x= 3/2

#SPJ3