SOLUTION: Solve, expressing your answer in exact, simplified form. log<sub>b</sub>x = log<sub>b</sub>(x – 5) – log<sub>b</sub>(x + 7)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve, expressing your answer in exact, simplified form. log<sub>b</sub>x = log<sub>b</sub>(x – 5) – log<sub>b</sub>(x + 7)      Log On


   

Question 61959: Solve, expressing your answer in exact, simplified form.
logbx = logb(x – 5) – logb(x + 7)
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The given expression is:

logbx = logb(x – 5) – logb(x + 7)

This can be further written as:

0 = logb(x – 5) - logb(x + 7) - logbx

This implies:

logb(x - 5) - (logb(x + 7)+ logbx) = 0

logb(x - 5)- logb((x + 7)(x)) = 0

logb((x - 5)/x(x + 7)) = 0

by the definition we get:

b%5E0 = x%2F%28x-5%29%28x%2B7%29

1 = %28x+-+5%29%2Fx%28x%2B7%29

x(x + 7) = x - 5

This implies:

x%5E2+%2B+7x+ = x - 5

x%5E2+%2B+6x+-+5+=+0+

On solving this, we get:

x%5E2+-+5x+-+x+-+5+=+0

(x - 5) (x - 1) = 0

Thus, x = 5, 1