Evaluate:

Let

Taking log on both side

⇒ log x = log ( (76.23)³ × ∛1.928 ) – log ((42.75)⁵ × 0.04623)

(∵ log a÷ b = loga – log b)

⇒ log x = log (76.23)³ +log ∛1.928 – (log (42.75)⁵ +log 0.04623)

(∵ log a × b = loga + log b)

⇒ log x = log (76.23)³ +log ∛1.928 – log (42.75)⁵ –log 0.04623

(since, log aⁿ = n log a)

⇒ log x = 5.6463 + 0.0950 – 8.1545 + 1.3350

⇒ log x = –1.0782 = ̅1.0782

⇒ x = antilog ̅1.0782 = 0.08352