What is log675 with base 5 × log 3 with base 3?
We have to calculate (log 675 to the base 5) × (log 3 to the base 3)
Note the following important points :
(1.) log 675 to the base 5
=> log 675 to the base ‘e’ / log 5 to the base ‘e’
=> ln 675 / ln 5
Since 675 = 5^2 × 3^3
=> ln 675 = ln [5^2 × 3^3]
=> ln (5^2) + ln (3^3)
=> 2 ln 5 + 3 ln 3
Hence, log 675 to the base 5
= ln 675 / ln 5
= [2ln 5 + 3ln 3] / ln 5
(2.) Similarly, log 3 to the base 3
=> Since the logarithm of any natural number 'x' to the base of same number 'x' is always 1 (since any natural number raised to the power '1′ is equal to the same number) ,
Thus, (log 3 to the base 3) = 1
Hence, our problem reduces to:
(log 675 to the base 5) × (log 3 to the base 3)
=> [(2ln 5 + 3ln 3) / ln 5] × (1)
=> (2ln 5 + 3ln 3) / ln 5
=> So we only require the values of natural logarithm of 3 and 5 :)
We should remember these values, or we can always use log table.
Since ln 3 = 1.098
and ln 5 = 1.609
=> 2ln 5 = 2(1.609) = 3.218
=> 3ln 3 = 3(1.098) = 3.294
Hence,
solution : (3.218 + 3.294) / 1.609
=> 6.512 / 1.609
=> 4.047
GLAD TO HELP YOU ;))
Answer:
13 14/15
Step-by-step explanation:
The numerator and denominator of 28/30 have a greatest common factor of 2. Dividing that from each of those numbers gives 14/15. This is the reduced fraction of the mixed number. The integer portion stays the same.
13 28/30 = 13 14/15
The length of a table, the width of a classroom, and the length of a car can be easily measured without using trigonometry (could probably use a meter stick or measuring tape) because we can easily reach both ends
the width of a wide river is a little different, it may not be practical to measure the distance across directly.
Answer:
36x
Step-by-step explanation:
You do 12 x 3 which equals 36. Then you add the x at the end.
