Answer:
㏒3(14) = 2.402 ⇒ 3rd answer
Explanation:
* Lets revise some rules of the logarithmic functions
- log(a^n) = n log(a)
- log(a) + log(b) = log(ab) ⇒ vice versa
- log(a) - log(b) = log(a/b) ⇒ vice versa
* Lets solve the problem
- We have the value of ㏒3(2) and ㏒3(7)
- We must change the problem to these logarithm to solve
∵ 14 = 2 × 7
∴ We can write ㏒3(14) as ㏒3(2 × 7)
∴ ㏒3(14) = ㏒3(2 × 7)
* Now lets use the rules above
∵ log(ab) = log(a) + log(b)
∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)
∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771
∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402
* ㏒3(14) = 2.402