Question

solve this-2^4x×4^3x-1=4^2x/2^3x​

Answer 1

Step-by-step explanation:

$2 ^{4x} \times {4}^{3x} - 1 = \frac{ {4}^{2x} }{ {2}^{3x} } \\ \\ 2 ^{4x} \times {2}^{6x} - 1 = \frac{ {2}^{4x} }{ {2}^{3x} } \\ \\ {2}^{4x + 6x} - 1 = {2}^{4x - 3x} \\ \\ {2}^{10x} - 1 = {2}^{x} \\ \\ {2}^{10x} - {2}^{x} = 1 \\ \\ {2}^{x}( {2}^{9x } - 1) = 1$

Therefore,

${2}^{x} = 1 \\ {2}^{x} = {2}^{0} \\ x = 0$

and

${2}^{9x} - 1 = 1 \\ \\ {2}^{9x} = {2}^{1} \\ \\ 9x = 1 \\ \\ x = \frac{1}{9}$