If 2 Log X + 1 = Log 360, Find: Log(2 X -2)

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

Sum

log(2 x -2)
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 (2x - 2)
= log(2.6 - 2)
= log 10
= 1.

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Chapter 10: Logarithms - Exercise 10.2

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