How do you solve $log(x+54) - log(x+2) = 2 - log(x)$ ?

Question

1756 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-01T09:46:04

$28+2sqrt 246$ =59.36877#, nearly

Use, $log ab= loga +logb and log(a/b)=loga -logb$

Rearranging.

$log((x(x+54))/(x+2))=2$

Inversely,

$((x(x+54))/(x+2))=10^2=100$ .

Cross-multiply, rearrange and solve for positive root..

$x^2-56 x- 200=0$

$x=28+2sqrt 246$ =59.36877#, nearly

How do you solve log(x+54) - log(x+2) = 2 - log(x)log(x+54) - log(x+2) = 2 - log(x)?