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)
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Question 61959: Solve, expressing your answer in exact, simplified form.
logbx = logb(x – 5) – logb(x + 7)
Answer by chitra(359) (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:
=
1 =
x(x + 7) = x - 5
This implies:
= x - 5
On solving this, we get:
(x - 5) (x - 1) = 0
Thus, x = 5, 1
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