Solve 2^ (x -3) - 8 = 0

The task is to find the value of x such
that:

2^ (x -3) - 8 = 0

We make use
of the laws of indices to separate the "x-3" index into 2 terms:

2^x
. 2^(-3)   -  8  = 0

Add 8 on both
sides:

2^x . 2^(-3)   =   8

2^x . 1/
2^(3) = 8

We know that 2^3 = 8:

2^x .
1/8 = 8

Multiply by 8 on both
sides:

2^x  = 64

We also know that 64
can be written as 2^6

2^x =
2^6

Comparing the
indices,

x=6

Counter
check

It is a good habit to counter check our answer by putting the
values back into the original equation:

LHS = 2^ (6 -3) - 8  =  2^3
-8  = 0 = RHS

Therefore, we confirm that x=6 is the
answer