Ignore the solution to the first question, there's a mistake in it.

log_c a + log_c b = log_c a.b

So,

log_2(x+7) + log_2(x) = 3

log_2{x^2 + 7} = 3

x^2 + 7 = 2^3 = 8

x^2 = 1

x={-1,1}

Don't forget to check the results because x+7 > 0 and x>0.

Ah, x = -1 doesn't satisfy x>0. So we remove it from the solution set.

x=1

----------------------------------------------

Let

Multiply both sides by a,

Put these a values back in ,

(Not real!)

(We exclude this because it's impossible to have such real x)