MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Fundamental Laws of Logarithms

Write down di...

Question

Write down different properties of logarithm.

Open in App

Solution

Logarithm laws
$\begin{matrix} P r o d u c t s : & l o g_{b} m n = l o g_{b} m + l o g_{b} n R a t i o s : & l o g_{b} \frac{m}{n} = l o g_{b} m - l o g_{b} n P o w e r s : & l o g_{b} n^{p} = p l o g_{b} n R o o t s : & l o g_{b} \sqrt[a]{n} = \frac{1}{q} l o g_{b} n C h a n g e o f b a s e s : l o g_{b} n = l o g_{a} n l o g_{b} a \end{matrix}$
$\begin{matrix} P r o p e r t y & D e f i n i t i o n & E x a m p l e P r o d u c t & l o g_{b} m n = l o g_{b} m + l o g_{b} n & l o g_{3} 9 x = l o g_{3} 9 + l o g_{3} x Q u o t i e n t & l o g_{b} \frac{m}{n} = l o g_{b} m - l o g_{b} n & l o g_{\frac{1}{4}} \frac{4}{5} = l o g_{\frac{1}{4}} 4 - l o g_{\frac{1}{4}} 5 P o w e r & l o g_{b} n^{p} = p l o g_{b} n & l o g_{2} 8^{x} = x . l o g_{2} 8 E q u a l i t y & i f l o g_{b} m = l o g_{b} n, t h e n m = n . & l o g_{a} (3 x - 4) = l o g_{a} (5 x + 2) s o, 3 x - 4 = 5 x + 2 \end{matrix}$

$l n e = 1 l o g_{a} a = 1 l o g_{a} x y = l o g_{a} x + l o g_{a} y l o g_{a} x^{p} = p l o g_{a} x \frac{d l n x}{d x} = \frac{1}{x} \frac{d^{n} l n x}{d x^{n}} = (- 1)^{n - 1} (n - 1)! x^{- n}$
$l n e^{x} = 1 l o g_{a} a^{x} = x l o g_{a} \frac{x}{y} = l o g_{a} x - l o g_{a} y l o g_{a} x = \frac{l o g_{b} x}{l o g_{b} a} \int \frac{1}{x} d x = l n x \int l n x d x = x l n x - x$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Define logarithm and write down different properties.

Q. Write down properties of teflon.

Q. Write down all properties of a line.

Write down the physical properties of Bases.

Q. The mantissa of

log 7623

^{.} 8821259;

write down the logarithms of

7^{.} 623, 762^{.} 2,^{.} 007623, 762300,^{.} 000007623 .

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Fundamental Laws of Logarithms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Fundamental Laws of Logarithms

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon