Let logb 2=2.217 and logb 3=3.417. Find logb 3b

Question

Please walk me through this steo by step.

Answer 1

One of the main rules of logs is this one:
log (AB) = log A + log B , as long as the base is the same in all log expressions.
We have that case here, everything is in terms of base b

so log_b (3b) = log_{b</sub 3 + logb</sub b
= 3.417 + 1 , since logb</sub b = 1
= 4.417}