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bezimeni [28]
3 years ago
14

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

<u>Step-by-step explanation:</u>

          2ˣ⁺² = 5²ˣ

      ln 2ˣ⁺² = ln 5²ˣ               <em>apply ln to both sides</em>

(x + 2) ln 2 = 2x ln 5            <em>apply exponent to coefficient log rule</em>

x ln 2 + 2 ln 2 = 2x ln 5       <em>distribute (x + 2) on left side</em>

2 ln 2 = 2x ln 5 - x ln 2        <em>subtract (x ln 2) from both sides</em>

2 ln 2 = x(2 ln 5 - ln 2)         <em>factor out (x) from right side</em>

\frac{2ln2}{2ln5 - ln2} = x                             <em>divide both sides by (2 ln 5 - ln 2)</em>


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