Question

Basics of Logarithm and Anti logarithm.

With proper explanation and example.

POINTS = 50 points. ​

Answer 1

Answer :-

So as it is asked for the Basics of Logarithm and Antilog .

♦ First of all

◾What is Logarithm ?

→ Logarithm is the representation of higher power in short values in order to solve the questions easily.

eg. We can write 2³ as log₂⁸ = 3

◾ What is Antilog ?

→It is the reverse function of Logarithm

eg. Antilog of log₂⁸ = 3

or 3 = log₂⁸

◾Now Some basics of Logarithm .

⏩ Representation of log

▪️We represent log of any number as .

$\star log_ba$

▪️It is called logarithm of a to the base b .

▪️Where :-

→(i) a > 0

→(ii)b > 0

→ (iii) b ≠ 1

◾Now the value of

$log_ba = c$

$\longrightarrow a = b^c$

◾Addition of log :-

$log_am + log_an = log_a(m\times n)$

▪️Similarly we can write

$log_n(m \times n) = log_a m + log_an$

◾Subtraction of log :-

$log_am - log_an= log_a(m\div n)$

▪️Similarly we can write

$log_a (m \div n) = log_a m - log_an$

◾Power of log :-

⏩Case 1 :

$log_am^n = (n)\:log_am$

▪️Similarly we can write

$(n)\:log_am = log_am^n$

⏩Case 2 :

$log_{a^k}m =( \frac{1}{k})log_am$

▪️Similarly we can write

$( \frac{1}{k})log_am =log_{a^k}m$

⏩Case 3 :

$log_{a^k}m^n = (\frac{n}{k})\:log_am$

▪️Similarly we can write

$(\frac{n}{k})\:log_am =log_{a^k}m^n$

◾Another results :-

$\star a^{log_cb} = b^{log_ca}$

$\star a^{log_ab} = b$

$\star log_ba = \dfrac{loga}{logb}$

$\star log_ba = \dfrac{1}{log_ab}$

◾Now some values of log with the base 10 :-

▪️$log_{10}\:1=0$

▪️$log_{10}\:2=0.3010$

▪️$log_{10}\:3=0.4771$

▪️$log_{10}\:4=0.6020$

▪️$log_{10}\:5=0.6990$

▪️$log_{10}\:6=0.7781$

→ We can find out other values from logarithm table .

Answer 2

Here is your answer❤️✌️✌️❤️

♈️✨✨The antilogarithm is the inverse function of a logarithm, so log(b) x = y means that antilog (b) y = x. You write this with exponential notation such that antilog (b) y = x implies by = x.

✨✨✨If log M = x, then M is called the antilogarithm of x and is written as M = antilog x.

For example, if log 39.2 = 1.5933, then antilog 1.5933 = 39.2.

If the logarithmic value of a number be given then the number can be determined from the antilog-table. Antilog-table is similar to log-table; only difference is in the extreme left-hand column which ranges from .00 to .99.

Mathematical properties of logarithms

Logarithms convert multiplication into addition and division into subtraction, and exponentiation into mulitplication:

log(A.B) = log(A) + log(B)

log(A/B) = log(A) - log(B)

log(An) = n.log(A)

log values☯️☯️

log 1 = 0

log 2 = 0.3010

log 3 = 0.4771

log 4 = 0.6020

log 5 = 0.6989

log 6 = 0.7781

log 7 = 0.8450

log 8 = 0.9030

log 9 = 0.9542

log 10 = 1

✍️✍️ please mark it brainlist Answer..