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Solution : 4 x^1 32 or ( 22 )x^1 32 , or, 22 x^2 25 ? 2 x 2 5 , or, 2 x 5  2 , or, 2 x 3 2 3 ?x ? Solution is 2 3 x Exercis ...

We know, 23 8 ; this mathematical statement is written in terms of log as log 28 3. Again, conversely, if log 28 3 , it can be w ...

Now,MN ax˜ay axy ?loga(MN) xy,orloga(MN) logaMlogaN [putting the values of x,y] ?loga(MN) logaMlogaN. (proved) Note 1.loga(M ...

Proof : We know, logaM logbMulogab [formula 5] Putting M a we get, logaa logbaulogab or 1 logbaulogbb; b a a b log 1 ?log or a b ...

or 4 2 22 4 a ( 20 ) {( 25 )} ( 2 5 ) or 4 4 a ( 25 ) ?a 25 ? the base is 2 5 Example 9. Find the value of x: (a)log 10 x  2 (b ...

0DWK,;;)RUPD [ log 10 1 ] (log 3 2 log 2 1 ) (log 3 2 log 2 1 ) 2 3 10 10 10 10 10      . 2 3 Exercise 4.2 Find the ...

4.6 Logarithmic Systems Logarithmic systems are of two kinds : (a) Natural Logarithm : The mathematician John Napier (1550 – 161 ...

We observe : Table-2 N Form au 10 m ofN Exponent Number of zeroes between decimal point and its next first significant digit Cha ...

Again, there is no zero in between decimal point and its next first significant digit of the number 0 ˜ 4305 , i.e. there is 0 z ...

Alternative : We use the calculator : AC ln 10 = 2 ˜ 30259 (approx). Activity : Find the logarithm of the following numbers (eac ...

Express into scientific form : (a) 6530 (b) 60 ˜ 831 (c) 0 ˜ 000245 (d) 37500000 (e) 0 ˜ 00000014 Express in the form of ordina ...

Chapter five Equations with One Variable We have known in the previous class what equation is and learnt its usage. We have lear ...

Again, the degree of each of the equations x^2  5 x 6 0 , y^2 y 12 , 4 x^2  2 x 3  6 x is 2 ; these are quadratic equations ...

0DWK,;;)RUPD Activity : 1. What is the degree of and how many roots has each of the following equations? (i) 3 x 1 5 2 3 ...

Example 2. Solve :(y 1 )(y 2 ) (y 4 )(y 2 ) Solution :(y 1 )(y 2 ) (y 4 )(y 2 ) or, y^2 y 2 y 2 y^2  4 y 2 y 8 or, ...

Example 5. Find the solution set : 2 x 3  5 2 Solution : 2 x 3  5 2 or, 2 x 3 2  5 [by transposition] or, 2 2 2 x 3  ...

By the question, 11 x 20 2 ( 11 x 2 ) 6 or, 11 x 20 22 x 4  6 or, 22 x 11 x 20  6  4 [by transposition] or, 11 x 22 or, ...

or, 2 x 80000 or,x 40000 ? Mr. Kabir invested Tk. 40000 at the rate of profit 12%. Activity : Solve by forming equations : What ...

Solve by forming equations (20 - 27) : A number is 5 2 times of another number. If the sum of the numbers is 98, find the two ...

An important law of real numbers is applied to the method of factorization. The law is as follows : If the product of two quanti ...