Question

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

Answer 1

Answer: 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

$\frac{2ln2}{2ln5 - ln2}$ = x                             divide both sides by (2 ln 5 - ln 2)