Question

If 2 log x + 1 = log 360, find: log (3 x² - 8)

Answer 1

log (3 x² - 8)
2logx + 1 = log360
⇒ logx² + log10 = log360
⇒ log(10x²) = log360
⇒ 10x² = 360
⇒ x² = `(360)/(10)` = 36

⇒ x = `sqrt(36)` = ±6
As negative value is rejected,
∴ x = 6
∴ log (3 x² - 8)
= log{3(6)² - 8}
= log(108 - 8)
= log100
= log10²
= 2log10
= 2 x 1
= 2.