Logarithms and exponents are pretty closely related.
What is '3 to the power 4'? It is '3 times 3 times 3 times 3'.
That will equal 81.
So the power of the base tells us
how many times the base is multiplied with itself.
We say that '3 raised to 4' equals 81.
We have studied this in exponents.
What are logarithms then?
Now this exact same thing can be written using logarithms.
This can be written as logarithm of 81 to the base 3 is equal to 4.
Yes, logarithm can also be written as log.
But look at this expression carefully.
The power or the exponent is the answer
and the base of the log is the base number.
So in the log expression,
we are asking '3 raised to what will give us 81'?
'3 raised to 4'.
The power to which the base of the log needs to be raised to,
to get the argument, will be the answer.
The power to which 3 needs to be raised to, to get 81, will be the answer.
It's 4.
Wasn't that simple?
Let's look at an interesting problem.
'Log of 125 to the base 5' is given to us as 'x'.
What is the value of 'x'? To get the answer
we should try writing this in the exponential form.
This asks us, '5 raised to what power gives us 125'?
'5 to the power x gives us 125'.
This makes it easier to find the value of 'x'.
We know that '5 times 5 times 5' is 125.
So '5 to the power 3 will equal 125'.
It gives us the value of 'x as 3'.
Let me give you two more examples.
I want you to pause the video and find the values 'x' and 'y'.
So how did you write the first equation in exponential form?
'2 raised to what gives us 32'?
'2 raised to the power x gives us 32'.
And we know that '2 raised to 5 equals 32'.
The value of 'x is 5'.
The second one is bit interesting.
The equation can be written as '4 raised to y is equal to 1'.
'4 to what power will result in 1'?
Do you remember a property of exponents?
Any non zero number raised to 0 will result in 1.
Hence, '4 raised to 0 will equal 1'.
The value of 'y is 0'.
