Question

What is the solution to the equation below?

log7+log(x-4)=1

Answer 1

Assuming log denotes base 10:

log 7 + log(x−4) = 1
=> log[7(x−4)] = 1
=> 7(x−4) = 10^1 = 10
=> x − 4 = 10/7
=> x = 4 + 10/7 = 38/7 ≈ 5.4286.

Check domain: x > 4, and 38/7 > 4, so it's valid.

(If log were base b, the solution would be x = 4 + b/7.)