solve log(5u^2+68u+143)-log(u+11)=7

Question

I did it but I'm not sure if it's correct

Answer 1

What we have here is a difference of logs.  We can write this as

 

 

log((5u² + 68u + 143) / (u + 11)) = 7

 

log((5u + 13 )(u + 11) / (u + 11)) = 7

 

log(5u + 13) = 7

 

The exponent is the solution to a logarithm.  The base of the exponent will be 10.

 

 

10⁷ = 5u + 13

 

10⁷ - 13 = 5u

 

(10⁷ - 13) / 5 = u