What is x if 4^(4x-15)-4=0 ?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve 4^(4x-15) - 4 = 0.

4^(4x-15) - 4 = 0

=> 4^(4x-15) = 4

=> 4^(4x-15) = 4^1

Now as the base is the same we can equate the power.

4x - 15 = 1

=> 4x = 15 +1

=> 4x = 16

=> x = 16/4

=> x = 4

Therefore x = 4.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll re-write the equation, moving the coefficient -4 to the right side:

4^(4x-15) = 4

We can write as well:

4^(4x-15) = 4^1

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

4x-15 = 1

4x = 15 + 1

4x = 16

We'll divide by 4:

x = 4

The solution of the equation is x = 4.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

What is x if 4^(4x-15)-4 = 0 ?

We add 4 to both sides and rewrite the given equation as below:

4^(4x-15) = 4

=> 4^(4x-15) = 4^1.

The bases on both sises are equal. So we equate the exponents on both sides:

4x-15 = 1

We add 15 to both sides:

4x = 1+15 = 16.

=> 4x /4= 16/4 = 4.

Therefore x = 4 is the solution.