plz tell me about the rules of logarithm to solve the questions in class 12th?

Rules of Exponents.

1

ak = a−k ak an = ak+n ak

an = ak−n a

b k

= ak

bk (ak)n = akn kpa = a1/k

Rewrite each of the following expressions in the form a b c .

1

a7 b2

a b c

2 at b5

cr a2 c3

b2 3

a2 b−2 pc

a3/2 b−3 c5 4 a3pb

c7 !5

Exponential and Logarithmic Functions.

A logarithm is the inverse of an exponential. That is, loga ax = x for any positive a 6= 1, and aloga x = x.

We usually use a base of e, which is natural constant (that is, a number with a letter name, just like ).

The number e is approximately 2.7182818284590452354. The logarithm we usually use is log base e, written

loge(x) or (more often) ln(x), and called the natural logarithm of x.

Rules of Logarithms.

• Definition: c = logb(a) () a = bc

• The Big One: ln(xy) = y · ln(x) or loga(xy) = y · loga(x)

• Others: loga(r · s) = loga(r) + loga(s) loga(r/s) = loga(r) − loga(s)

loga(b) =

logx(b)

logx(a) , for any x

Solve for t (algebraically, not numerically) in the following equations.

5 200 = 5 t3 6 800 = 4 · 7t 7 400 = 200 + 3 · 2t 8 432 = 100e0.6t

9 log2(t) = 6 10 ln(t2) = 30

Functions of Exponential Type.

A function is said to be of exponential type if it can be written in the form

y = a · bt where a and b are constants.

If we are given two data points, (two pairs of t and y values), we can determine the constants a and b by

solving a system of two equations.

Example: Given that 200 = a · b2 and 450 = a · b7, we divide the second equation by the first to

get:

450

200

= b7

b2 and so 9/4 = b5, giving b = 5p9/4.

Substituting that into the first equation gives a =

200

(9/4)2/5 = 200 · (9/4)−2/5.

Find a and b given that:

11 30 = a · b5 and 80 = a · b9 12 1.5 = a · b24 and 2.3 = a · b36

(1) a6 b1 c−1 (2) at+2 b3 c3−r (3) a1/2 b1 c−9/2 (4) a15 b5/2 c−35 (5) t = 3 p40 (6) t = log7 (200) (7) t = log2 (200/3) (8)

t = (ln 4.32) /0.6 (9) t = 26 (10) t = e15 (11) b = (8/3)1/4 , a = 30 · (8/3)−5/4 (12) b = (2.3/1.5)1/12 , a = (1.53 )/(2.32 ) .

if you didn’t under stand A word log into that:

(http://www.math.toronto.edu/mathnet/SOAR2003/Winter/PDF/logs.pdf)

Logarithms are exponents, powers of a base number. For example 100 can be written as 10^2 (10 squared or 10 x 10). So, the Logarithm of 100 using 10 as a base is 2. This is written as:

Log 100 = 2

Because 10 squared = 100.

(The base number is assumed to be 10 if it isn’t written)

So, log 1000 = 3

and log 7 = .845 because 10^.845 = 7

Using logarithms simplifies some mathematic operations.

If you add logs you are multiplying the numbers they represent. When you subtract them, you are dividing the numbers they represent.

So: 100 * 7 = 700 which can be expressed as:

10^2 + 10^.845 or 10^(2 + .845) = 10^2.845

so log 100 + log 7 = 2.845

I’m sure that your text book will have a very complete explanation. I suggest you take a look at it from the beginning and work some of the problems.