Answer my query on logarithm?

Question

log b(to the base a)=log b(to the base c)/log a(to the base c)
does this c represent any number.
what is e.
what is log a(to the base e.)

Answer 1

The logarithm equation you presented is the change of base law.

C can be any number, commonly 10 or e as our calculators only work in bases of 10 or e and this law helps to solve log equations of other bases.

e is the natural logarithm number (its like the concept of pi, e= approx. 2.71....)

Answer 2

e is a special number defined as follows-
e = 1+ 1/1! + 1/2! +-----------to infinity
value of e is approximately 2.7.....
if a=e^x then x = log a(to the base e)

if a^x = b then we say log b(to the base a)=x
let a^x=b & c^y=a
so, y=log a(to the base c)
now b= a^x = (c^y)^x = c^(xy)
so, log b(to the base c) =xy = log b(to the base a) * log a(to the base c)
hence
log b(to the base a) = log b(to the base c)/ log a(to the base c)

Answer 3

that is the formula for converting a logarithm of a number in one base to the logarithm of another base.

Answer 4

e is a constant. Its value is 2.7... It has the special property
that the derivative of the function e^x is itself.

log(b,a) = log(b,c)/log(a,c)

The above formula is always true. So a,b,c can be any positive number.

Basically e to the power of log(a,e) = a or e^log(a,e) = a

a^log(b,a) = b
c^log(a,c) = a
c^log(b,c)=b

Now,

a^log(b,a) = b

so
(c^log(a,c))^log(b,a)=b
so
c^(log(a,c)log(b,a))=b
so (log(b,c)=log(a,c)log(b,a)
So log(b,a)=log(b,c)/log(a,c)

Answer 5

the first one: it means a=b=c
second one: e is a number that was used to oftern (approx...2.178.......) so it was named "e"...log e = ln
third one: ln a