Question

4^x + 16^x = 3 find .....plz slove it i will make his/her ans as brainlist

Answer 1

${4}^{x} + {16}^{x} = 3 \\ {2}^{2x} + {2}^{4x} = 3 \\ {2}^{2x} (1 + {2}^{2x} ) = 3 \\ let \: {2}^{2x} = y \\ y(y + 1) = 3 \\ {y}^{2} + y = 3 \\ {y}^{2} + y - 3 = 0 \\ y = \frac{ - 1 + - \sqrt{ {1 }^{2} + 4 \times 3 } }{2} \\ y = \frac{ - 1 + - \sqrt{ {13}} }{2} \\ y = \frac{ \sqrt{13} - 1}{2} \\ {2}^{2x} = \frac{ \sqrt{13} - 1 }{2} \\ 2x log(2) = log( \sqrt{13} - 1 ) - log(2) \\ x = \frac{log_{2}( \sqrt{13} - 1 ) - 1}{2}$
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Answer 2

Hi Mate!!!

put 4^x =t

t² + t - 3 =0

t = -1 + √13 / 2 or t = -1 - √13 /2


x = Log ( -1 +√13 / 2 ) / Log ( 4 )

or

x = Log ( -1 -√13 / 2 ) / log ( 4 )