**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: 10^{4} = 10000, so log_{10}10000 = 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 = b^{y}, then y = log_{b} (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.

There are four basic rulers to be followed and they are given away as follows,

log

log_{a} x/y = log_{a} x – log_{a} *y*

log_{a} x^{n} = *n*log_{a} x

Log_{a}b = log_{c}b/log_{c}a

log3 5 + log3 40 – 3 log3 10

2 log3 5 + log3 40 – 3 log3 10

= log3 5^{2} + log3 40 – log3 10^{3}

= log3 25 + log3 40 – log3 1000

= log3 `(25*40)/1000`

= log3 1

= 0

Given that log2 3 = (1.585) and log2 5 = (2.322), evaluate log4 15

Log4 15 =` ((log2 15)/(log2 4))`

= `(log2 (3*15))/(log2 22)`

= `(log2 3 + log2 5)/(2log2 2)`

= (1.585) +`2.322/2`

=(1.9535)

Evaluate 2 log3 27 + log3 81 – 3 log3 9

Solution:

=2 log_{3} 3^{3} + log_{3} 3^{4} – 3 log_{3} 3^{2}

= 3*2log_{3} 3 + 4log_{3} 3 – 2*3log_{3} 3

= 6log_{3} 3 +4log_{3} 3– 6log_{3} 3

=6(1) + 4(1) -6(1)

=10-6

=4