Question

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

Answer 1

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.