1.

\operatorname { log } _ { 13 } ( 2 ^ { x + 2 } - 4 ^ { x } ) \geq - 2

Answer»

eliminating the log to the R.H.S

=> 2^(x+2) -4^x ≤ (1/3)^-2 => 4.2^x -(2^x)² ≤ 9=> (2^x)² -4.2^x +9 ≥0

let 2^x = t

=> t²-4t+9 ≥ 0 ∆ = 4²-36 = -ve...so this equation is always +ve..

so x ==> R


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