log_{7}(x-sqrt(x^{2}-21))+log_{7}(x+sqrt(x^{2}-21)) i tried multiplying but i keep getting different answers
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$\displaystyle log_{7}(x-\sqrt{x^{2}-21})+log_{7}(x+\sqrt{x^{2}-21})$ $\displaystyle log_{7}[(x-\sqrt{x^{2}-21})(x+\sqrt{x^{2}-21})]$ $\displaystyle log_{7}(x^{2}-(x^{2}-21))$ $\displaystyle log_{7}(21)$
Originally Posted by grillage $\displaystyle log_{7}(x-\sqrt{x^{2}-21})+log_{7}(x+\sqrt{x^{2}-21})$ $\displaystyle log_{7}[(x-\sqrt{x^{2}-21})(x+\sqrt{x^{2}-21})]$ $\displaystyle log_{7}(x^{2}-(x^{2}-21))$ $\displaystyle log_{7}(21)$ Why is it not Log_{7}(-21)? because the x^{2} cancles and you are left with -21? my aswer choices are 1. log3 7 2. log7 3 3. 7 + log7 3 4. 1 + log7 3 5. 1 + log3 7
The 21 is inside the bracket so you have a double minus making a plus $\displaystyle log_{7}(21)=log_{7}(7)+log_{7}(3)$ $\displaystyle 1+log_{7}(3)$
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