Struggling with Logarithmics? Let’s fix that.
I’ve noticed a lot of students posting questions online (especially on Reddit) and either getting no replies… or answers that don’t actually explain the method clearly.
Let’s do things differently here.
Here’s a quick one to get started:
Solve:
log₂(x − 1) + log₂(x − 3) = 3
Try it yourself first - then check the approach below:
Combine logs:
log₂[(x − 1)(x − 3)] = 3
Convert to exponential form:
(x − 1)(x − 3) = 2³ = 8
Expand and solve:
x² − 4x + 3 = 8
x² − 4x − 5 = 0
Factorize:
(x − 5)(x + 1) = 0
Final answer:
x = 5 (valid), x = -1 (reject - outside domain)
Key takeaway: Always check domain restrictions in logs.
-1 isn't accepted because it's outside the domain...? How did you know that?
Glad you asked…-1 is rejected because logarithms only accept positive values inside. Here we need x-1>0 and x-3>0, which gives x>3. Since −1 doesn’t satisfy this, it’s outside the domain...
hope you understand…please go ahead if you require detailed understanding or we can discuss in today’s Webinar…