সপ্তম অধ্যায়ঃ লগরিদম

Properties of Logarithm

1. If [tex] y = a^x [/tex], then [tex] \log_a y = x [/tex]. → Definition of logarithm

2. [tex] \log_a xy = \log_a x + \log_a y [/tex]

3. [tex] \log_a \dfrac{x}{y} = \log_a x - \log_a y [/tex]

4. [tex] \log_a x^n = n \log_a x [/tex]

5. [tex] \log_a a = 1 [/tex]

6. [tex] \log_a 1 = 0 [/tex]

7. [tex] \log_{10} x = \log x [/tex] → Common logarithm

8. [tex] \log_e x = \ln x [/tex] → Naperian or natural logarithm

9. [tex] \log_y x = \dfrac{\log x}{\log y} = \dfrac{\ln x}{\ln y} [/tex] → Change base rule

10. If [tex] \log_a x = \log_a y [/tex], then [tex] x = y [/tex].

11. If [tex] \log_a x = y [/tex], then [tex] x = anti\log_a y [/tex].

সমাকলনবিদ্যা

1. [tex]\displaystyle \int du = u + C[/tex]

2. [tex]\displaystyle \int a \, du = a\int du[/tex]

3. [tex]\displaystyle \int (du + dv + ... + dz) = \int du + \int dv + ... + \int dz[/tex]

4. [tex]\displaystyle \int f (x)\,dx = F(x) + C[/tex]

[tex]\int f (x)\,dx = F(x) + C[/tex]

[tex]\int_a^b f(x) \, dx = F(b) - F(a)[/tex]

[tex]\int_a^b f(x) \, dx = -\int_b^a f(x) \, dx[/tex]

[tex]\int_a^b f(x) \, dx = \int_a^c f(x) \, dx + \int_c^b f(x) \, dx[/tex]

1. বীজগণিত, 2. স্থানাঙ্ক জ্যামিতি, 3. অন্তরকলনবিদ্যা , 4. সমাকলনবিদ্যা , 5. সমাকলনবিদ্যা , 6. কলনবিদ্যার প্রয়োগ

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