00:01
In the given question we have a few logarithmic equations and we are told to solve each of this equation.
00:09
So first we have equation a which is given as log x is equal to 2.
00:16
So to solve for log and to solve for x what we need to do is to use a property of logarithm that says a raised to the power log with base a.
00:30
Of x is equal to x.
00:35
So how do we use this property? so what we are going to do is to write both sides of this equation as powers of a number.
00:44
And the number we take is the base of the logarithm in the question.
00:49
So if the base of the logarithm is not mentioned, it is understood that the base of it is 10.
00:56
So generally we take the base of logarithm as 10 and that's why we don't write 10 with logarithm whenever we use it in its general form.
01:08
So now since this is the case, what we are going to do is to take the, take both sides of this equation as powers of 10.
01:20
So log with base 10, 10 to the power log x is equal to 10 to the power 2.
01:33
And this would simplify using the property over here we can simplify this as x is equal to 10 square, which means we have the solution of the given equation as x equal to 100.
01:51
So this is how we solve this logarithmic equation...