Indian Institute of Technology

Algebra Level 3

6 + log ⁡ 3 2 ( 1 3 2 4 − 1 3 2 4 − 1 3 2 4 − 1 3 2 . . . ) = ? 6 + \log _{ \frac { 3 }{ 2 } }{ \left( \frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4 - \frac { 1 }{ 3\sqrt { 2 } } ... } } } \right) } = \ ?


The answer is 4.

Priyanshu Mishra by Priyanshu Mishra , 20, India

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1 solution

Prakhar Bindal
Dec 13, 2016

Call that thing inside log (square root part) to be x

by observation

x = square root (4-x/3root2)

solve it as a quadratic in x

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Prakhar Bindal , Thanks i got it now.

Priyanshu Mishra - 4 years, 6 months ago

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