Question

1+2+2²+2³+...+2^x=1023

Answer 1

$1 + 2 + 2^{2} + 2^{3} + 2^{x} = 1023 \\3 + 4 + 8 + 2^{x} = 1023 \\7 + 8 + 2^{x} = 1023 \\15 + 2^{x} = 1023 \\2^{x} = 1023 - 15 \\2^{x} = 1008 \ln(2^{x}) = ln(1008) \\xln(2) = ln(16 * 8 * 7) \\xln(2) = ln(2^{4} * 2^{3} * 7) \\\frac{xln(2)}{ln(2)} = \frac{4ln(2) + 2ln(3) + ln(7)}{ln(2)} \\x = 4 + \frac{2ln(3)}{ln(2)} + \frac{ln(7)}{ln(2)}$