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

Mathematics

1 answer:

GenaCL600 [577]3 years ago

4 0

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)

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