Need Help. The question is down below These are NOT answer choices

Please show your work for each of these problems

Useful Log Rules:

Part (a)

All logs shown below are base 3.

log(500) = log(5*100)

log(500) = log(5*10^2)

log(500) = log(5)+log(10^2) use log rule 1

log(500) = log(5) + 2*log(10) use log rule 3

log(500) = 1.4650 + 2*2.096 substitution

log(500) = 5.657

Part (b)

All logs shown below are base 3.

log(2) = log(10/5)

log(2) = log(10) - log(5) use log rule 2

log(2) = 2.096 - 1.4650   substitution

log(2) = 0.631

50=33x+22

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for