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:
<em>c. 13.899.79</em>
Step-by-step explanation:
<u>Exponential function
</u>
Two variables y and x have an exponential relation if
where C and k are real numbers. Many natural phenomena are modeled by using exponentials, finance included, where the growing of the investments can be computed through the use of the exponential function
The situation described in the question is modeled as
being A is the total value of the investment, p is the initial value of the investment, and n is the number of years the money is invested. We know p=2,500 and n=18, so we compute A
Answer: c. 13.899.79
Answer:
375 adult tickets and 302 student tickets
Step-by-step explanation:
s+a=677
a=s+73
s+s+73=677
2s+73=677
2s=604
s=302
a= 375
Answer:
Step-by-step explanation:
A horizontal cross section of a cone will be circle
