3 x 2^x+3 = 192 x 3^x-3

Question

How to solve and simplify this? 

Answer 1

We use * to show multiplication instead of × because of the confusion with the variable x.

 

So I assume you mean 3 * 2^(x+3) = 192 * 3^(x-3), where I put what I think are the exponents in parentheses. Without those parentheses you would have a much different problem.

 

Divide both sides by 3:

2^(x+3) = 64 * 3^(x-3)

 

Change 64 to a power of 2:

2^(x+3) = 2^6 * 3^(x-3)

 

Divide both sides by 2^6:

2^(x+3-6) = 3^(x-3)

 

Divide both sides by 3^(x-3):

(2^(x-3))/(3^(x-3)) = 1

 

(2/3)^(x-3) = 1 = (2/3)^0

 

Same base on both sides so equate exponents:

x-3 = 0

 

x = 3

 

Check:

3 * 2^(3+3) =? 192 * 3^(3-3)

3 * 2^6 =? 3 * 2^6 * 3^0

3 * 2^6 = 3 * 2^6 * 1 √