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express-the-following-in-form-of-log-a-f-x-i-4log-a-x-log-a-x-2-x-3-ii-log-a-x-log-a-x-3-




Question Number 9334 by j.masanja06@gmail.com last updated on 30/Nov/16
express the following in form of log a(f(x))  (i) 4log_a x−log_a (x^2 +x^3 )  (ii) log_a x +  log_a (x+3)
$$\mathrm{express}\:\mathrm{the}\:\mathrm{following}\:\mathrm{in}\:\mathrm{form}\:\mathrm{of}\:\mathrm{log}\:\mathrm{a}\left(\mathrm{f}\left(\mathrm{x}\right)\right) \\ $$$$\left(\mathrm{i}\right)\:\mathrm{4log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} \right) \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{log}_{\mathrm{a}} \mathrm{x}\:+\:\:\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}+\mathrm{3}\right) \\ $$
Answered by mrW last updated on 30/Nov/16
(i)⇒4log_a x−log_a (x^2 +x^3 )=log _a ((x^4 /(x^2 +x_  ^3 )))=log _a ((x^2 /(1+x)))  (ii)⇒log_a x +  log_a (x+3)=log _a [x(x+3)]
$$\left(\mathrm{i}\right)\Rightarrow\mathrm{4log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{3}} \right)=\mathrm{log}\:_{\mathrm{a}} \left(\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{x}_{\:} ^{\mathrm{3}} }\right)=\mathrm{log}\:_{\mathrm{a}} \left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}}\right) \\ $$$$\left(\mathrm{ii}\right)\Rightarrow\mathrm{log}_{\mathrm{a}} \mathrm{x}\:+\:\:\mathrm{log}_{\mathrm{a}} \left(\mathrm{x}+\mathrm{3}\right)=\mathrm{log}\:_{\mathrm{a}} \left[\mathrm{x}\left(\mathrm{x}+\mathrm{3}\right)\right] \\ $$

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