Question

Solve for x:

log 2x + log 6 = 1 + log 12

Answer 1

log 2x + log 6 = 1 + log 12

We know that 1 = log ⁡10  ....(since base = 10)

log 2x + log 6 = log 10 + log 12

Using the rule log⁡ a + log ⁡b = log ⁡(ab),

log (2x × 6) = log (10 × 12)

log (12x) = log (120)

Since the logarithms are equal, their arguments are equal:

12x = 120

x = `120/12`

x = 10