Prove that: 2 log (35/192) + 2 log (114/91) + log 48 + 2 log (13/19) = log (75/64)
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Step-by-step explanation:
Given: 2 log(35/192) + 2 log(114/91) + log48 + 2log(13/19)
= log(35/192)² + log(114/91)² + log48 + log(13/19)²
∴ aⁿbⁿ = (ab)ⁿ
= log[(35/192)*(114/91)]² + log48 + log(13/19)²
= log[95/416]² + log48 + log(13/19)²
= log[9025/1730156] + log48 + log(13/19)²
∴ log a + log b = logab
= log(48 * 9025/1730156) + log(13/19)²
= log(27075/10816) + log(13/19)²
= log(27075/23104)
= log(75/64)
I hope this help you!
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