Solve for x : `log_2 x + log_4 x + log_8 x + log_16 x = 25`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation `log_2 x + log_4 x + log_8 x + log_16 x = 25` has to be solved for x

`log_2 x + log_4 x + log_8 x + log_16 x = 25`

=> `log_2 x + (log_2 x)/(log_2 4) + (log_2 x)/(log_2 8) + (log_2 x)/(log_2 16) = 25`

=> `log_2 x + (log_2 x)/2 + (log_2 x)/3 + (log_2 x)/4 = 25`

=> `(25/12)(log_2 x) = 25`

=> `(log_2 x) = 12`

=> `x = 2^12`

The value of x = `2^12`

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