What is the exact solution to the equation 2^x+2 =5^2x ? a) −2ln2/2ln5−ln2 b) −ln2/2ln5+ln2 c) ln2/2ln5+ln2 d) 2ln2/2ln5−ln2

We want to get the exact solution for the equation:

The correct option is D, the solution is:

Here we must use the property:

So we can apply the natural logarithm to both sides of our equation to get:

Now we can solve this for x.

So the correct option is D.

If you want to learn more, you can read:

link

D

Step-by-step explanation:

          2ˣ⁺² = 5²ˣ

      ln 2ˣ⁺² = ln 5²ˣ               apply ln to both sides

(x + 2) ln 2 = 2x ln 5            apply exponent to coefficient log rule

x ln 2 + 2 ln 2 = 2x ln 5       distribute (x + 2) on left side

2 ln 2 = 2x ln 5 - x ln 2        subtract (x ln 2) from both sides

2 ln 2 = x(2 ln 5 - ln 2)         factor out (x) from right side

= x                             divide both sides by (2 ln 5 - ln 2)