lg1+lg2+lg4+lg8+...+lg1024
=lg1+lg2+lg2^2+lg2^3+...+lg2^10
=0+lg2+2lg2+3lg2+...+10lg2
=lg2*(1+2+3+……+10)
=55lg2
log(以2为底)10
=lg10/lg2
=1/lg2
所以原式=55