Answer

Verified

430.5k+ views

**Hint:**Here we will logarithmic properties to find the value of \[\log 25\]. First we will write the 25 which is in the log function as a fraction. Then we will simplify it using the logarithmic properties. We will simplify it further and substitute the given logarithmic values. Then we solve the equation to get the required value.

**Complete step-by-step answer:**First, we will write the \[\log 25\] in the modified form by writing the number 25 in a different form. Therefore, we get

\[\log 25 = \log \dfrac{{100}}{4}\]

Now we will use the property of the logarithmic function i.e. \[\log a - \log b = \log \dfrac{a}{b}\].

Therefore, by using this property, we get

\[ \Rightarrow \log 25 = \log 100 - \log 4\]

We know that number 100 is the square of number 10 and number 4 is the square of number 2. Now we will write this in the above equation, we get

\[ \Rightarrow \log 25 = \log {10^2} - \log {2^2}\]

Now by using the property \[\log {a^b} = b\log a\], we get

\[ \Rightarrow \log 25 = 2\log 10 - 2\log 2\]

We know that the value of \[\log 2\] is given in the question and we know that \[\log 10 = 1\]. Therefore, we get

\[ \Rightarrow \log 25 = 2\left( 1 \right) - 2\left( {0.3010} \right)\]

Now we will solve the above equation to get the value of \[\log 25\]. Therefore, we get

\[ \Rightarrow \log 25 = 2 - 0.6020\]

\[ \Rightarrow \log 25 = 1.3980\]

**Hence, the value of \[\log 25\] is equal to \[1.398\].**

**Note:**Here in this question, we have to modify the number in the main equation according to the given values of log in the question. We should know that the value inside the log function should never be zero or negative it should always be greater than zero. Always remember that the value of the \[\log 10\] is equal to 1. We should simplify the equation carefully and apply the properties of the log function accurately.

Some of the basic properties of the log functions are listed below.

1.\[\log a + \log b = \log ab\]

2.\[\log {a^b} = b\log a\]

3.\[\log a - \log b = \log \dfrac{a}{b}\]

4.\[{\log _a}b = \dfrac{{\log b}}{{\log a}}\]

Recently Updated Pages

Who among the following was the religious guru of class 7 social science CBSE

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Trending doubts

Derive an expression for drift velocity of free electrons class 12 physics CBSE

Which are the Top 10 Largest Countries of the World?

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE

The energy of a charged conductor is given by the expression class 12 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Derive an expression for electric field intensity due class 12 physics CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Derive an expression for electric potential at point class 12 physics CBSE