log(3(108))+log(3(3/4))?

Question

i need help with this equation: log(3(108))+log(3(3/4)). the answer is 5, but I'm stomp on the work. Can someone show a step by step procedure on how this happens?

and also

e^(ln3)+e^(ln2)-e^(lne) this one just made me confused. help anyone?

Answer 1

Question 1
This is not an equation as there is no = sign.
Let log mean log to base 3 in the following :-
log 108 + log (3/4)
log (108 x 3/4)
log (81)
4

Question 2
e^ ln3 + e^ln 2 - e^1
3 + 2 - e
5 - e

Answer 2

log(3(108))+log(3(3/4))
= log(3(108(3/4))
= 5log3
= 5 if the base is 3.

e^(ln3)+e^(ln2)-e^(lne)
= 3+2-e
= 5-e

Answer 3

im asuming the 3 is the base of the log, for the first one u cud plug in (log108/log3) + [log(3/4)/log3) in ur calculator. the "/" means divide. i kno thats obvious but juts in case. if u gotta do it by hand u gota join the logs:

log(3(108))+log(3(3/4))
log(base3)(108*(3/4))
log(base3)81 now change it to exponential form
3^(x)=81
3^(x)=3^(5)
x=5

for the second one, every time u have "e" elevated to an ln the cancel out. its lik havin log (base 2) 2 , they cancel out n become one:

e^(ln3)+e^(ln2)-e^(lne)
3(1)+2(1)-e
5-e

if some one else gives u another answer id go wit that one cuz im not 100 % sure bout it, im only in 10th grade

Answer 4

If you have difficulties in converting numbers from one base to another, this will help.
The log to a certain base of a number is equal to the log to another base of the number divided by the log to the new base of the old base, or

log to base a of b = (log to base c of b) / (log to base c of a).

If you have a good scientific calculator, try it with some examples to prove that it works.