# What is x if 113^(3x-4)-1/113^(x-12)=0?

neela | High School Teacher | (Level 3) Valedictorian

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What is x if 113^(3x-4)-1/113^(x-12)=0.

We multiply both sides by 113(x-12):

113(3x-4)*113(x-12) - 1 = 0, as (a^m)*(a^n) = a^(m+n) by exponent rule.

113^(3x-4+x-12) = 1.

113^(4x-16) = 1 = 113^0.

113^(4x-16) = 113^0.

Since the bases are  same, the exponents must be equal.

=> 3x-16 = 0.

=> 4x= 16.

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

=> x = 4.

So x= 4 is the solution.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll use the negative power property of exponentials:

1/113^(x-12) = 113^-(x-12)

Now, we'll re-write the equation:

113^(3x-4) - 113^-(x-12) = 0

113^(3x-4) = 113^-(x-12)

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

3x - 4 = -x + 12

We'll isolate x to the left side. For this reason, we'll add x both sides and we'll add 4 both sides:

3x + x  = 12 + 4

We'll combine like terms :

4x = 16

We'll divide by 4:

x = 4

The solution of the equation is x = 4.