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Solve logarithm equations with procedureQ22-23?

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22. log(5x)-2 = log(x+1) log(5x) - log(x+1) = 2 log [5x/(x+1)] = 2 log 10 . . . . . . . . 《Formula: log 10 =1》 log [5x/(x+1)] = log 102 . . . . . . . . .《Formula: x log a = log a?》 5x/(x+1) = 102 5x = 100x + 100 -100 = 100x - 5x 95x = -100 ∴ x = -100/95 = -20/19 23. (a) log(3x+2y) = 1 log(3x+2y) = log 10 . . . . . . . . 《Formula: log 10 =1》 3x+2y = 10 2y = 10-3x ∴ y= 5 - (3/2)x = 5 - 3x/2 (b) 2 logx - 5 log y = 0 2 logx - 5 log y = log 1 . . . . . Reason: log 1 = log 10° = 0*(log 10) = 0*1 = 0 =>《Formula: log 1 =0》 log x2 - log y? = log 1 . . . . . .《Formula: log a? = x log a》 log (x2/y?) = log 1 . . . . . .《Formula: log a/b = log a - log b》 x2/y? = 1 x2 = y? ∴ y = x2/?

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