Question

Give your answer to four decimal places

Answer 1

Answer:

The characteristic of a logarithm is the number to the left of the decimal.

(The characteristic is like an exponent).

We are working with base 3 logs.  

So if we are increasing a number by multiplying it by the base of the logarithm, (in this case 3 times 3)  then we increase the characteristic by two.

Since 2 is the exponent of 3^2 then to get the log 3 of 72, we get the log3 (8) and increase it by 2.

1.8928 +2 = 3.8928

Had we been working with base 10 logs and we were multiplying a number by 100, We would increase the characteristic by 2 because 100 = 10^2.

Step-by-step explanation: