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Question Number 26117 by ibraheem160 last updated on 20/Dec/17

(1/6)(√((3log1728)/(1+(1/2)log36+(1/3)log8)))  simplify the question above

$$\frac{\mathrm{1}}{\mathrm{6}}\sqrt{\frac{\mathrm{3}{log}\mathrm{1728}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{log}\mathrm{36}+\frac{\mathrm{1}}{\mathrm{3}}{log}\mathrm{8}}} \\ $$$${simplify}\:{the}\:{question}\:{above} \\ $$

Answered by ajfour last updated on 20/Dec/17

=(1/6)(√((9log 12)/(1+log 12)))   =(1/2)(√((log 3+2log 2)/(1+log 3+2log 2))) .

$$=\frac{\mathrm{1}}{\mathrm{6}}\sqrt{\frac{\mathrm{9log}\:\mathrm{12}}{\mathrm{1}+\mathrm{log}\:\mathrm{12}}}\: \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\mathrm{log}\:\mathrm{3}+\mathrm{2log}\:\mathrm{2}}{\mathrm{1}+\mathrm{log}\:\mathrm{3}+\mathrm{2log}\:\mathrm{2}}}\:. \\ $$

Commented by ibraheem160 last updated on 20/Dec/17

but the final is (1/2)

$${but}\:{the}\:{final}\:{is}\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

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