Question
Question: How do you solve \(\log x+ \log 20=2\) ?...
How do you solve logx+log20=2 ?
Solution
We are given an equation involving two logarithmic functions and a constant term. Thus, we must have basic knowledge of the logarithmic functions in order to solve this equation. Firstly, we will apply the basic properties of logarithm on the logarithmic terms on the left-hand side of the equation to convert them into a single term. Further, we shall take the antilogarithm on both sides to finally find the solution for x.
Complete step-by-step solution:
We are given the equation logx+log20=2.
We know by the well-defined properties of logarithm that when the sum of two logarithmic functions is given, then it can also be written as the log of product of those two functions and if the logarithm of product of two log functions is given, then it can also be written as the sum of logarithm of those two functions.
It is expressed as loga+logb=logab and logab=loga+logb respectively.
Here, we have a=x and b=20. Thus, we have
⇒log20x=2
Taking antilog on both sides, we get
⇒20x=e2
Now, we shall divide both sides by 20,
⇒x=20e2
Therefore, the solution of logx+log20=2 is x=20e2.
Note: Whenever a log is written in any mathematical equation, it represents the logarithm with base of exponent, e. If the base of the logarithm is something else such as 10 or some other constant, then it is specifically written in the equation along with the log. However, if the base is not specified then we take the base as e, by default.