log 36/6 + log 3/2 - log 6/5 ? assume all logs are to the base 3.Simplify?

Answer 1

Since log x + log y = log (x*y):

log 36/6 +log 3/2 - log 6/5 = log (6*3*5/(2*6))=log15/2

Answer 2

log (a/b) = log a - log b (rule 2 of logarithm)
note 36/6 = 6
= log 6 + (log 3 - log2) - ( log 6 - log 5)
= log 6 + log3 - log 2 -log 6 + log 5
note 6 = 3x2
log (ab) = log a +log b (rule 1)
log 6 = log (3x2) = log 3 + log 2
= log 3 + log 2 + log 3 - log 2 - (log 3 + log 2) +log 5
= 2 log 3 - log 3 - log 2 + log 5
= log 3 + log 5 - log 2
log a + log b + log c = log (axbxc) = log (abc)
= log (3x5) - log 2
= log 15/2 (All to base 3)

If you want to get a numeric answer you have to change the base form 3 to anyone calculatable with am using base 10
log (base 3) of 15/2 = y
3 (to the power of) y = 15/2
; log both sides (base 10)
symbol '^' = indext power or raised to power of
log 3^y = log (15/2)(all in base 10)
log A^y = y log A (rule 3)
y log 3 = log (15/2)
y = log (15/2) / log 3
y = (log 15 - log 2) / log 3
y = log 15 - log 2 - log 3
log 15 = log (3x5) = log 3 + log 5
y = log 3 + log 5 - log 2 - log 3
y = log 5 - log 3 (all in base 10)

log 5 = 0.69897000433601880478626110527551...
log 3 = 0.47712125471966243729502790325512...

y = 0.698970 - 0.477121
y = 0.221849
(approx) y = 0.222

Answer 3

log 36/6 + log 6/5 = log ( (36/6) * (3/2) ) = log 9
log 9 - log 6/5 = log ( (9) / (6/5) ) = log (15/2)

All base 3

Answer 4

(log 3 + log 2 ) - (log 3 + log 2 - log5) +(log 3 - log 2)
== log 5 + log 3 - log 2 == log 15/2

Answer 5

= log [ (6 x 3/2) / (6/5) ]
= log[ (6 x 3 x 5 ) / (6 x 2) ]
= log(15/2)
= log15 - log 2
= log (15/2)
= log(7.5)

Answer 6

log x + log y = log (x*y) so you can combine the first two together.

log x - log y = log (x/y) so you can use this to combine the result with the third log.

You'll end up with log(something) where the something has lots of multiplications and divisions which are easily done.