Introduction to solving 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 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.

Let us see method for solving logarithms homework and some problems and propertires of logarithms homework.

 

Set of laws in solving logarithms homework:

 

The logarithm of a to the base b is written logb(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.

The exercise of logarithms to make easy complicated calculations was a significant impulse in their original development. Logarithms have applications in fields as assorted as statistics, chemistry, physics, astronomy, computer science, economics, music, & engineering.

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

    if= loga x – loga y

3) Power Rule

    loga xn = nloga x

4) Change of Base Rule

    Logab = logcb/logca

 

Home work problems on solving logarithms homework:

 

Problem 1:

Solve for x  : log2x = 6

Solution:

Given, log2x = 6

We know that  logba = c  then `b^c = a`

log2x = 6

   2^6 = x

   64 = x

  x = 64.

Answer:  x =64

 

 

Problem 2:      

Solve for m:3m = 1000

Solution:

Given 3m = 1000

Take log on both sides,

 log 3m = log 1000

m log 3 = log 10^3

m ( 0.477) = 3 log 10

m(0.477) = 3 (1) 

Divided by 0.477 on both sides,

 m = 3 / 0.422

 m = 7.1