How to solve exponential equation. 5(3-2^(2-X)) = -65

Question

The 2-X is in the exponent

Answer 1

5(3-2^(2-x))=-65

Step1. Divide both sides of the equation by 5.

5(3-2^(2-x))=-65

-----------   ------

      5               5

After division we got 

3-2^(2-x)=-13

Step2. Now susubstract 3 on both sides of the equation.

3-2^(2-x)-3=-13-3

-2^(2-x)=-16

Remove negative sign from both sides of the equation.

2^(2-x)=2⁴ 

Step 3.Remove the common base .

2-x=4

Step 4. Substract 2 on both sides of the equation.

2-x-2=4-2

After substitutions we have .

-x=2

Step 5. Now multiply both sides by negative sign.

-(-x)=-2

Therefore the final answer is

x=-2 

 

Answer 2

5(3-2^∧(2-x)) = - 65;  3-2^∧(2-x) = -13;  - 2^∧(2-x) = - 16;  2^∧(2-x) = 16 = 2⁴  so  2-x = 4;  x = -2