Question

Prove that: 2 log (35/192) + 2 log (114/91) + log 48 + 2 log (13/19) = log (75/64)​

Answer 1

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!