On the top, use the power rule (see other post I answered).

x ln 7 = x + 7 ln 6

That is a messy equation.

Divide each side by (x + 7).

According to a logarithmic rule (whose name alludes me),

.

Then solve with your calculator with decimal place for 2 places.

That "logarithmic rule" probably doesn't exist so you better wait for another answer.

For the second problem,

Remember that log 10 = 1.

The solve.

I don't know what it means by

Be sure to reject any value that is not in the domain of the original logarithmic expressions.means dont give a decimal because it's probably a fraction or square root.

"Give an exact answer."