Question

Solve for x:

log (x – 5) + log 4 = 2

Answer 1

We are given:

log(x – 5) + log 4 = 2

Step 1: Combine the logs

log[4(x – 5)] = 2

Step 2: Convert to exponential form

4(x – 5) = 10² = 100

Step 3: Solve for x

4(x – 5) = 100

x – 5 = 25

x = 30

Step 4: Check validity

• x – 5 = 25 > 0 → valid

x = 30