Question

If 2 raised to the power x+5 = (2 raised to the power x+7) +3. Find the value of x

Answer 1

The value of x is (-0.5)

Explanation:

•Given expression is

(x+5)² = (x+7)²+3 ..(1)

•Therefore,(x+5)² is in the form of (a+b)²

•As we know the formula of (a+b)² =a²+b²+2ab

•Then,

(x+5)² = x²+25+10x ..(2)

(x+7)² = x²+49+14x ..(3)

•Substituting (2),(3) in equation (1),we get

x²+25+10x = x²+49+14x +3

•By solving,

x²+25+10x-x²-49-14x-3 = 0

-24-4x+22 = 0

-4x-2 = 0

4x+2 = 0

x = (-2/4) = (-1/2) = (-0.5)

•Therefore,the value of x is -0.5