Karteikarten
Logarithm
Karten in diesem Stapel (10)
- 1Loglog a (b)
It is defined for b>0 and a>0 a≠1 - 2Properties of loglog a (1)=0
log a (a)=1
log a (x*y)=log a (x)+log a (y)
log a(x/y)=log a (x)-log a (y)
log a (b^n)=n*log a (b)
log a^n (b)=1/n log a (b)
a^log a (b)=b
a^log b (c)=c^log b (a)
log b (a)=1/log a (b)
log b (a)=log a/log b - 3Some conceptsNever reduce the degree of variable used.
For equations like a^x=b^y
a=b=1 or x=y
For logs with no base given we can choose 10 as base.
(a^n)^n=(a^n)^2
Root of x^2 is equal to mod of x.
In ratio take k as common multiple then take 10 as base and solve question.
While solving exponents base should be equal.
While solving polynomials multiply numbers first then variable used. - 4Inequalities in loglog a (x)>log a (y)
If a>0,x ∝ y
If 0 - 5Solving problems related to inequalities in log1.Equate bases of log in L.H.S and R.H.S.
2.Check the validity of variable used.
3.Solve the inequality,if base is variable then take cases of variable that is,greater than 0 but less than 1 and greater than 1 or take case of values obtained in validity.
4.Solution is the intersection of value obtained and validity. - 6DomainThese are those x for which given equality or inequality is defined.
- 7How to find number of digits in a number ?We can find number of digits in a number by making the number to base 10.
Remember-
log 10 (2)=0.3010
log 10 (3)=0.4771
For eg 10^9 has 10 digits. - 8Inequalities in log with different bases and numbersWe can solve inequalities in log with different bases and numbers by estimating it,s result.
- 9Natural logln=log e
- 10Comparing logsLog should be compared with the same base.
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- Karteikarten am Logarithm, erstellt von Prajjwal Sanskar am 25/04/2018.
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- Prajjwal Sanskar
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