Phillip R. answered • 08/18/14

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I use two rules which you should memorize.

First, if A and B are numbers greater than zero, then log A + log B = log AB.

This rule combines two logs into one.

Second, if log X = Y, then by definition, 10

^{Y}= XThis rule changes a log equation into an exponential equation.

So starting with log X + log (X + 15) = 2, we use the first rule to get

log [X(X + 15)] = 2

using the second rule, we get

10

^{2}= X(X + 15)Now we can solve for X

X

^{2}+ 15X - 100 = 0(X - 5) (X + 20) = 0

Therefore X = 5 or X = -20

The answer X = -20 is eliminated because if we use it in the original equation we get log (-20) which is undefined because the domain of the log function is X > 0.

So we have one answer X = 5