Question

How do i solve 2? Rewriting the equation so that you set up a one to one correspondence between all of the parts. Then solve for x

Answer 1

rewrittenOur original equation:

`((1)/(2))^x=\text{ 8}`

We need to find the value of x, so if x>1 the result will never get 8 because the exponent:

`((1)/(2))^6=((1)^6)/((2)^6)=(1)/(64)`

So, let's use a negative exponent:

In this case -3, because 2^3= 2*2*2=8.

`((1)/(2))^(-3)=((1)^(-3))/((2)^(-3))=((1)/(1^3))/((1)/(2^3))`

Operate and solve:

`((1)/(1))/((1)/(8))=(8)/(1)=8`

So, rewriten equation:

`((1)/(2))^x=((1)/(2))^(-3)`

Solution:

x= -3