Do-This


(1)write the following in logoarthemetic form

(i)7=2r (ii)10=5b (iii)181=3c (iv)100-10z (v)1257=4a
(2)Write the following inexponential form.

(i)log10100-2 (ii)log525=2 (iii)log22=1

Try this
solve the following.
(i)log232=x (ii)log5625=y (iii)log1010000=z (iv)logx16=2 :.x2=16_vx=+4,Is it correct or not?


can we say "exponential form and logoarthim"form are inverse of one another?

Also,observe every positive real number has unique logoarthemetic value,because any horizontal line touches the graph at one point.


Think and discuss.

(1)Does log20exist?Give reasons.
(2)Prove (i)logbb=1 (ii)logb1=0 (iii) logxbx=x 




Properties of Logarithms
       

Logarithms are more important in many applications,and also in advanced mathematics.we now,establish some basic properties useful in manuplating expressions involving logarithms.

       
(i)The product rule

       
The properties of exponents correspond to properties of logarithms.For example when we multiply with same base,we add ecponents

.i.e  axayax+y


           This property of exponents coupled with an awareness that a logarithm is exponent suggest theproduct rule.

Therom:(product rule)let a,x and y be positive resl number with a=/1


           
Then log axy=logax+logay

           i.e The logarithm of a product is the sum of logarithm.
           
proof:

         
 let logax=m,and logay=n then we have am=x,and an=y

           


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