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) \\(xln(2))/(ln(2)) = (4ln(2) + 2ln(3) + ln(7))/(ln(2)) \\x = 4 + (2ln(3))/(ln(2)) + (ln(7))/(ln(2))`