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Question Number 9334 by j.masanja06@gmail.com last updated on 30/Nov/16

$$\mathrm{express}\mathrm{the}\mathrm{following}\mathrm{in}\mathrm{form}\mathrm{of}\log \mathrm{a}\left(\mathrm{f}\left(\mathrm{x}\right)\right)$$$$\left(\mathrm{i}\right){4\log }_{\mathrm{a}}\mathrm{x}-{\log }_{\mathrm{a}}({\mathrm{x}}^2+{\mathrm{x}}^3)$$$$\left(\mathrm{ii}\right){\log }_{\mathrm{a}}\mathrm{x}+{\log }_{\mathrm{a}}(\mathrm{x}+3)$$

Answered by mrW last updated on 30/Nov/16

$$\left(\mathrm{i}\right)\Rightarrow {4\log }_{\mathrm{a}}\mathrm{x}-{\log }_{\mathrm{a}}({\mathrm{x}}^2+{\mathrm{x}}^3)=\log {}_{\mathrm{a}}\left(\frac{{\mathrm{x}}^4}{{\mathrm{x}}^2+{\mathrm{x}}_{}^3}\right)=\log {}_{\mathrm{a}}\left(\frac{{\mathrm{x}}^2}{1+\mathrm{x}}\right)$$$$\left(\mathrm{ii}\right)\Rightarrow {\log }_{\mathrm{a}}\mathrm{x}+{\log }_{\mathrm{a}}(\mathrm{x}+3)=\log {}_{\mathrm{a}}\left[\mathrm{x}(\mathrm{x}+3)\right]$$

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