What is x if 11^(5x-6)=1/11^(-x-10)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the equation 11^(5x-6)=1/11^(-x-10) to solve for x.

11^(5x-6)=1/11^(-x-10)

=> 11^(5x - 6) = 11^[-( - x - 10)]

=> 11^(5x - 6) = 11^(x + 10)

as the base is the same we can equate the exponent.

5x - 6 = x + 10

=> 5x - x = 10 +6

=> 4x = 16

=> x = 16/4

=> x = 4

Therefore x = 4

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

1/11^(-x-10) = 11^-(-x-10)

Now, we'll re-write the equation:

11^(5x-6) = 11^-(-x-10)

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

5x - 6 = x + 10

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

5x - x - 6 = 10

We'll combine like terms and we'll add 6 both sides:

4x = 10 + 6

4x = 16

We'll divide by 4:

x = 4

The solution of the equation is x = 4.

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