Now we need to find the value of logarithms
without using a calculator.
We will be using this formula right there,
so log b of b to the x is equal x.
So as long as we have the same number here
b and b then we always get the exponent.
So Let see how we gonna do example 1.
Example 1 log 2 of 16 so our goal is to write
16 as 2 to a number.
So we can have the 2 and 2.
so 2 to 4 is equal 16 right.
So log2 of 16 is equal log 2 of 2 to the 4
and the answer will be the exponent.
So it's 4.
Now log 2 of 8 same way log 2 and 8 is 2 cube
again we have 2 and 2 so the answer is the
exponent so 3.
Log 3 of 27 again we try to write 27 as 3
to a number 27 is 3 cube so the answer is
the exponent so it's also 3.
Log 3 of 81 same thing 81 is 3 to the fourth
3 times 3 is 9 times 9 is 81 so the answer
gonna be the the exponent so it's 4.
log 9 of 81 is log 9 81 is 9 squared so the
answer is the exponent so it's 2.
Now we trying to do for example 6 we have
fractions when we have fractions we do it
almost the same way 1 over 16 is the same
thing as1 over 2 to the 4.
But there is one extra step we move 2 to the
4 to the numerator so it become 2 negative
4. and then the answer is the exponent which
is negative 4.
Same thing for example 7 1 over 81.
81 is 3 to the 4 and then 3 to the 4 is the
same thing as 3 negative 4 so the answer is
the exponent negative 4. and the last example
example 8 log 9 81 is the same thing as 9
squared which is equal to log 9 negative 2
the base is also 9 the answer is the exponent
negative 2.
And now for example 9 instead of having log
2 of 16 we have log 16 the base is bigger
than the input in that case we always use
the radical or the root so what we do we try
to write some kind of root of 16 that will
give us 2.
Now which root of 16 will give us 2 is fourth
root of 16 now how what does that mean fourth
root of 16 it means 16 to 1 over 4 I am using
this formula.
Let me write it here n root of x is equal
x 1over n and the answer will be the exponent.
So it's 1 over 4.
now log 16 of 4 so we gonna do the same thing
since 16 is bigger then 4 we need to write
some root of 16 and of course it's just square
root of 16.
square root of 16 is 4.
Now, this is the same thing as log 16 16 1
half we're using the same formula again the
answer will be the exponent it's 1 half.
Here's another one here, log 81 of 3.
And we need some kind of root of 81 that will
give us 3 so it's the fourth root of 81 because
3 times 3 times 3 times 3 is 81 and this is
log 81 of 81 to the 1 fourth and the answer
will be the exponent which is 1 fourth so
that's enough example for you I mean finding
the value of logarithms.
