the definition of locker
allows us to least its basic properties
property number one says that look at it
into the base
a of one is Seattle and talk about it
into the base
a of a he spun as long as ace positive
and different than what
you might ask why is that well
low cut it into the base a of one ease
and exponent to which a has to be raised
to get 1 and that exponent
has to be said so look at it to the base
a of one is see it since
aid to the power one is who
eighty then law got it done to the base
a of a ease one and therefore
no matter what the failure of the base
of the Federal Credit them
Eve the number we take the low cut it of
ease
one then to look at it eases 0 so look
at them to the base to a plan
use 0 look at it to me or the base
E on natural know about it of one East
or so
Senate if they're number we take them
look at it
of matches the babys that's the second
property that tense as a
satcher lockout it is one so
blockaded was debased 15 of 15 is one
and natural log of E is also one
because it has the base E property
to and city op properties that
will follow from the fact that
exponential function and their low cut
it makes functions
are inverse functions so property number
two
says that composition of the exponential
function which there are no credit check
function
is an identity as long as an is greater
than
0 so if you have the expression that
is an exponent with the base a and that
exponent that base
easy days still the power low cut it
into the base a
out then there is solid is the number
that we take their low cut it of debt
exponentiation and taking clock at it
some actions
constantly chap so for example you have
six to the power located them six
up seven six and to look at it I'm 6'1
to the actions will cancel each other
and to end up just with seven the same
waved a
eat all the power and an A for scenes
and then of arm is it is there no credit
with the base
him eat property
if city tells us that composition of
their low cut it moved the exponential
functions identity
so if we need to take your a low cut it
with the base
a of the exponent that has base a
then again the logarithm and exponents
will consular a.m.
each other s fires action is concerned
and will end up just with the input
of show if I have low cut it into the
base for the anti want to take that
lockout at them of city to the power for
the dance is going to be just for
and the same with them look at it of e2
the power 2x the ancel that is going to
be 2x
the first part of property far simply
says that look at it
to their base pay is a function if we
have equal
input should end the outputs are going
to be the same but this will allow us to
call from the equation
X ke quarter for to the equation log
to the base a all X equals
rock to the bay's a golf for
we would say that weekend its
are not take a look at it of both sites
of the equation the second part
is the one to one property of and
logarithmic function if to lock out its
more of the same base a
called into the inputs a call so if I
have the quotation local to the base for
X mine
swine secord I'll cut it into the base
for of 2x minus
5 that then I can write that
X -1 will have to be 2x
minus 5 as long as X the SATs
that they also got it deems exist
