Question

Product property:
logbxy = logbx + logby

How would you expand log412 so that it can be evaluated, given log43 ≈ 0.792?


Log Subscript 4 Baseline 3 times log Subscript 4 Baseline 4 StartRoot a squared + b squared EndRoot

log 3 + log 4

log Subscript 4 Baseline 3 + log Subscript 4 Baseline 4

log 3 times log 4

Answer 1

Use the product rule with 12 = 3·4:

log_4 12 = log_4(3·4) = log_4 3 + log_4 4.

Since log_4 4 = 1, this is log_4 3 + 1 ≈ 0.792 + 1 = 1.792.

So the correct expansion is log_4 3 + log_4 4 (which simplifies to log_4 3 + 1).