How do you solve log_5 x + log_10 x = 4?

1 Answer
Mar 25, 2016

x=44.228

Explanation:

As log_b x=log_ax/log_ab, we have

log_5x+log_10x=4 can be written as

log_10x/log_10 5+log_10x=4 or

log_10x/0.699+log_10x=4 or

log_10x+0.699xxlog_10x=4xx0.699 or

log_10x(1+0.699)=4xx0.699 or

log_10x=(4xx0.699)/1.699=1.6457

x=10^(1.6457)=44.228