solve for x

x = (5 log(2)+6 log(5))/(log(2)+log(5))

x=5.6990

10^(x-5)=5   take the log of both sides

log 10^(x - 5)  = log 5   and we can write

(x - 5) log 10   = log 5       and log 10 = 1, so we can ignore this part.....and we have.....

x - 5 = log 5       add 5 to both sides

x = 5 +  log 5  ≈  5.69897