#### Question

# Log of 81 to the base 27?

pls help

#### Answers

You can rewrite log of 81 to the base of 27 in base 10 by the 'change of base property' as (log81)/(log(27).

log81 = log(3^4) = 4log3 (Using the power rule)

log27 = log(3^3) = 3log3 (Using the power rule)

Therefore, (log81)/(log27) = (4log3)/(3log3) = 4/3

1.33333

http://www.1728.org/logrithm.htm

log 81 =log 81 log 27

27 10 / 10

= 4log 3 3 log 3

10 / 10

= 4/3

=1.333

log of 81 to the base 27 = log81 / log27 =

= log(3^4) / log(3^3) = 4*log3 / 3*log3 =

= 4/3 >==========================< ANSWER

Log A base X = Log A base Y / Log X base Y ........Rule

Therefore, log of 81 to the base 27 = log 81 / log 27 = 1.333333333

Rewrite log of 81 to the base of 27 in base 10 as (log81)/(log(27).

log81 = log(3^4) = 4log3

log27 = log(3^3) = 3log3

So, (log81)/(log27) = (4log3)/(3log3) = 4/3