Logarithms and indices

 

Good day my students, you're all welcome, today , i will teach you how to solve algorithms and it relationship with indices.Algorithms is one of those core mathematics that has to do with rules, and its operations. If you want to be the best in solving algorithms, you must be familiar with the instructions given. 

There are are some rules you have to understand before thinking of solving algorithms and how to manipulate any questions based on algorithms ans indices. Something like:

n² = n x n  

 3² = 9  is log₃ 9 = 2

 

                           1                                1               

 also 10⁻¹ is  --------   then log₁₀    ---------  =   - 1        

                        10                               10   

           

49 = 7² then log₇  49 = 2

144 = 12² then log₁₂  144 = 2

Note : If  P² = Z hence , log p  Z = 2

Now you can see, all the algorithms has their rules

to carry them during operation.

Like the ones we will solve together, just pay attention you will understand them.

 R² = T hence ,   log r T = 2 , 4² = 16 hence, log₄ 16 = 2  and so on......

Now lets simplify some algorithms

Solve the following

i. log₁₀  100

ii. log₄ 16

iii. log₅ 125

               1

iv. log --------

              25

Solution

i. log₁₀  100

    Let  log₁₀  100 = y ....make sure after = is letter  (from A -- Z)

    Let  log₁₀  100 = x

  

    10ˣ  = 100

   10ˣ   = 10²

    x = 2 ------ 10 and 10 is 1,so remove them to fix x and 2.

ii. log₄ 16

      Let log₄  16 =  x  you can change the letter x and use any letter of your choice....

    

     4ˣ  =  16

     4ˣ   =  4²

     x  =  2 ----- 4 and  4 is 1.........

iii. log₅ 125

  

Let  log₅ 125 = x

    5ˣ  =  125

        

    5ˣ  =  5³

   x  =  3 

     

                        1

iii. Let  log₅ -------- = n 

                       25

  

                    1

      5ⁿ  = ----------- 

                  25

                 1

     5ⁿ = ---------

                5²

  

      5ⁿ   =  5⁻²

    

   n   =   - 2     remember  5⁻² is 1/5² , we just remove the 2 fives to fix n and - 2.

   Relationship Between Algorithms and Indices

The operation involved in this mathematics is changing from algorithm to indices or indices to algorithms

Logₑ B = x ------- logarithms pattern .

eˣ = B ----Indices pattern

        log₅ 125 = x algorithm form

      5ˣ   =  125 ------ indices form

Lets write the following indices in algorithm form

i. 2ˣ = 3

ii. 7²   = 49

iii. 8² = 64

             Solution

    i. 2ˣ = 8

        log₂ 8 = x

 

ii.    7²   = 49

        log ₇  49 = 2  

    

iii.   8² = 64

       log₈  64 = 2

Lets write the following algorithms in indices form

i.. logₑ 27 = 3

                    1

ii.  log ₄₉ --------- 

                    2

iii. log₁₀  x = -1

   

 Solution

i.. logₑ 27 = 3

     e³  = 27

                        1

ii.  log ₄₉  y --------- 

                       2

  49¹⁺² =  y

iii. log₁₀  x = -1

      10⁻¹ = x

I believe you understand my lesson, just try and understand the common ideas behind this mathematics. 

If you have any question, please put them in the comments box.