Question

How to use log in maths? Give hints

Answer 1

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♣ LOGARITHMS

✍️ In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

♣FORM

✍️ $log_ab$

where,

a > 0 , a ≠1 , b > 0

✍️Read as " log of b to the base a ".

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♣ PROPERTIES

✍️ If $log_ab=c$

then,

$b={a}^{c}$

✍️ $log_mn=log_am+log_an$

✍️$log_a(m/n)=log_am-log_an$

✍️ $log_a{m}^{n}=nlog_am$

✍️$log_aa=1$

✍️$log_a1=0$

✍️${a}^{log_am}=m$

✍️$log_am=(log_bm/log_ba)$

✍️$log_{a}^{p}m=log_am/p$

✍️${a}^{(log_bm)}={m}^{(log_ba)}$

✍️ $log_am=1/log_ma$

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Now,

✍️LOGARITHMS are used to solve tticky and tough problems.

✍️we can use them to simplify complex integrals.

✍️ Also used in solving complex differentials.
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Answer 2

Log full form is Logarithm

First of all what is log

if log ( base a) b = c

then a^c = b

Now here 0<a <1 or a>1

and b should be positive

Now lets see Graph of it

As we know any no in between 0 and 1 raise to the increasing powers ,it will keep on decreasing

So log ( base 0<a<1) b will be decreasing function

And for a>1 its increasing as now no greater than 1 raise to increasing powers will keep on increasing

Now Properties

Log ab = log a + log b ( a and b should be positive)

log a^b = b log a ( here b can be negative also )

log a/b = log a - log b

MOST IMPORTANT for Jee is

log ( base a) b = log ( any base c) b)/ log ( any base c) a

In hindi it means "people" so it is meant for all people

✌✌✌Dr.Dhruv✌✌✌❤❤❤❤❤❤❤❤❤❤❤❤