Question

8^x-8^x-1=24 find x​

Answer 1

${8}^{x} - {8}^{x - 1} = 28 \\ {( {2}^{3} )}^{x} - {( {2}^{3}) }^{x - 1} = 28\\ {2}^{3x} - {2}^{3x - 3} = 28 \\( {2}^{3x} )(1) - ( {2}^{3x} )({2}^{ - 3}) = 28 \\ {2}^{3x} (1 - {2}^{ - 3} ) = 28\\ {2}^{3x} (1 - \frac{1}{ {2}^{3} } ) = 28 \\ {2}^{3x} (1 - \frac{1}{8} ) = 28 \\ {2}^{3x} ( \frac{7}{8} ) = 28 \\ {2}^{3x} = 28 \times \frac{8}{7} = 4 \times 8 = 32 = {2}^{5} \\ {2}^{3x} = {2}^{5} \\ 3x = 5 \\ x = \frac{5}{3}$

Answer 2

The answer of X= 5/3 and the value is 0.6