How do you prove #log_10 x +log_10(3x-5)=log_10 2#?

1 Answer
Cesareo R.
May 18, 2016

Not proof but calculation. #{x=-1/3,x=2}#

Explanation:

You cannot prove because it is not an identity. You can calculate or solve the proposition. Then let us calculate.
#log_ax+log_a(3x-5)-log_a2=log_a((x(3x-5))/2)=0#
But #log_ay=0->y = 1# So we get as a result
#((x(3x-5))/2)=1#. Now solving for #x# we get
#{x=-1/3,x=2}# two solutions.

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