Introduction to Logarithms Homework:

In mathematics, the logarithm to a number to a given base is the exponent to which the base should be raised in order to produce that number. For example, the logarithm of the function has 10000 to base 10 is 4, because 4 is the power to which ten should be raised to produce 10000: 104 = 10000, so log1010000 = 4. Only positive real numbers contain real number logarithms; negative & complex numbers have complex logarithms.
The logarithm of a to the base b is written log b(a) or, if the base is implicit, as log(a). So, for a number a, a base b and an exponent y,
If a = by, then y = logb (a)
The bases used often are 10 for the common logarithm, & e for the natural logarithm, & 2 for the binary logarithm. Here it is about the logarithms homework with example problems and practice problems. 

Logarithms Homework - Basic laws in Logarithm:

 

There are four basic rulers to be followed and they are given away as follows,
1) Product Rule
            loga xy = loga x + loga y
 
2) Quotient Rule
            loga x/y = loga x – loga y
 
3) Power Rule
            loga xn = nloga x
 
4) Change of Base Rule
            Logab = logcb/logca
        

 

Logarithms Homework - Example Problems:

 

Logarithms Homework - Example 1:

log3 5 + log3 40 – 3 log3 10

Solution:
2 log3 5 + log3 40 – 3 log3 10
= log3 52 + log3 40 – log3 103
= log3 25 + log3 40 – log3 1000
= log3 `(25*40)/1000`
= log3 1
= 0
Logarithms Homework - Example 2:
Given that log2 3 = (1.585) and log2 5 = (2.322), evaluate log4 15
Solution:
Log4 15 =` ((log2 15)/(log2 4))`
= `(log2 (3*15))/(log2 22)`
= `(log2 3 + log2 5)/(2log2 2)`
= (1.585) +`2.322/2`
=(1.9535)
 
Logarithms Homework - Example 3:
 
Evaluate 2 log3 27 + log3 81 – 3 log3 9
Solution:
=2 log3 33 + log3 34 – 3 log3 32
= 3*2log3 3 + 4log3 3 – 2*3log3 3
= 6log3 3 +4log3 3– 6log3 3
=6(1) + 4(1) -6(1)
=10-6
=4