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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You have provided the equation to be solved as 22^ (x -3) - 8 = 0.

I think it should be 2^ (x -3) - 8 = 0, and have changed the question accordingly.

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

Now add 8 to both the sides

=> 2^(x-3) = 8

express 8 as 2^3

=> 2^(x-3) = 2^3

we can now equate x-3 and 3

=> x-3 = 3

=> x = 6

Therefore the solution for 2^ (x -3) - 8 = 0 is x = 6.

Top Answer

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

2^(x-3) - 8 = 0

First we will add 8 to both sides:

==> 2^(x-3) = 8

Now we will rewrite 8:

we know that:

8 = 2^3

==> 2^(x-3) = 2^3

Now since the bases are equal, then the powers are equals too.

==> (x-3) = 3

==> x = 3 + 3 = 6

Then the answer is x = 6

changchengliang's profile pic

changchengliang | Elementary School Teacher | (Level 2) Adjunct Educator

Posted on

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

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since we have 2^(x-3), we'll apply the quotient rule:

a^(b-c) = a^b/a^c

We'll put a = 2, b = x and c = 3

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

But 2^3  = 8

2^(x-3) = 2^x/8

We'll re-write the equation:

2^x/8  -  8 = 0

We'll multiply by 8 both sides:

2^x - 64 = 0

We'll add 64 both sides:

2^x = 64

We'll write 64 as a power of 2:

64 = 2^6

2^x = 2^6

Since the bases are matching, we'll apply one to one property:

x = 6

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve 2^(x-3) -8 = 0.

We add 8 to both sides:

2^(x-3) = 8. We write 2^3  for 8 on the right side.

2^(x-3) = 2^3.

Since both sides of the equation has exponents to the same base 2, we equate the exponents of 2 of both sides:

x-3 = 3.

Add 3 to both sides:

x = 3+3 = 6.

Therefore x = 6 is the solution of 2^(x-3) - 8 = 0.

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