Solve each logarithmic equation. Check for extraneous solutions

Question

log42 = log21 +log(x-1)

Answer 1

Just use your log rules:

log42 = log21 +log(x-1)
log 42 = log (21(x-1))
42 = 21(x-1)
etc, make sure x>1 to have a valid answer

Answer 2

Log42 = Log21 + Log(x-1)
Log(x-1) = Log(42)-Log(21) = 0.30103.
x-1 = 10^(0.30103) = 2.0,
X = 2 + 1 = 3.