InterviewSolution
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InterviewSolution
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Solve `(8^x+27^x)/(12^x+18^x)=7/6` |
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Answer» Correct Answer - `x = -1 or 1` `(8^(x) + 27^(x))/(12^(x) + 18^(x) )=(7)/(6)` or `(8)^(x)/(12)^(x) ((1 +(27//8)^x))/((1 +(18//12)^x))= (7)/(6)` or `((2)/(3))^(x)((1 +(3//2)^(3x))/(1 +(3//2)^x))= (7)/(6)` Let `((3)/(2))^(x) = t` . Then `(1 +t^(3))/(t(1 + t)) = (7)/(6)` or `((1 +t)(t^(2) + 1 - t))/(t(1 + t)) = (7)/(6)` or `(t^(2)+ 1 - t)/(t) = (7)/(6) (because t + 1 ne` 0) or `6t^(2) - 13t + 6 = 0` or `(2t - 3)(3t-2) = 0` `rArr t = (2)/(3) or (3)/(2)` `rArr x = - 1 or 1` . |
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