#log_3 0.1 + color(red)(2log_3 x) = log_3 2 + log_3 5" "larr# use the power law
#:.log_3 0.1 + color(red)(log_3 x^2) = log_3 2 + log_3 5#
#color(blue)(log_a b + log_a c = log_a (b xxc))" "larr# multiply law
#:.log_3 0.1 xx x^2 = log_3 2 xx 5#
#log_3 0.1x^2 = log_3 10#
#color(darkviolet)(log A = log B hArr A = B)#
#:. 0.1x^2 = 10#
#x^2 = 10/0.1#
#x^2 = 100#
#x = +-sqrt100#
#x = +10 " or " x = -10#
Usually log of a negative number is invalid, but in this case, even if #x = -10#, when it is squared it becomes positive.
