Solving Equations with e and lnx We know that the natural log function ln(x) is de ned so that if ln(a) = b then eb = a. The common log function log(x) has the property that if log(c) = d then
Solution: If f(x) = g(x) f ( x) = g ( x) ,then: ln(f(x)) = ln(g(x)) → ln(ex) = ln(3) l n ( f ( x)) = l n ( g ( x)) → l n ( e x) = l n ( 3) Use log rule: loga xb = bloga x log a x b = b log a x, then: ln(ex) = xln(e) →
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Let’s take a look at a couple of examples. Example 1 Solve each of the following equations. 2log9(√x)−log9(6x−1) = 0 2 log 9 ( x) − log 9 ( 6 x − 1) = 0 logx+log(x −1) = log(3x
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