
Solve the algebraic expression for .
(a)
(b)
(c)
(d)
Answer
460.2k+ views
Hint: Take log to the base b, i.e., , both the sides and use the formula to simplify the expression. Now, use the product to sum-rule the logarithm given as: - for further simplification. Use the algebraic identity: - and cancel the like terms to get the answer.
Complete step by step solution:
Here, we have been provided with the logarithmic equation: - and we are asked to find the value of x.
Taking log to the base b, i.e., both the sides and using the formula: - , we get,
Using the product to sum of logarithm given by the formula , we get,
Rearranging the terms we can write the above expression as: -
Using the algebraic identity: - , we get,
Taking (-1) common in the L.H.S., we have,
Cancelling the common factors on both the sides, we get,
Using the formula , we can write the above expression as: -
Now, we can see that the base of the logarithm on both sides are the same, so we can equate their arguments by removing the log function. Therefore, we have,
Hence, option (c) is our answer.
Note: One may note that it will be difficult for us to solve the question in the exponential form and that is why we took the help of log to solve the question. The reason for taking log to the base ‘b’ was that we can clearly see that we had as the exponent on both sides of the original equation. Even if you will take any other base value you will need the base change rule given as: - to convert it into base ‘b’ at last.
Complete step by step solution:
Here, we have been provided with the logarithmic equation: -
Taking log to the base b, i.e.,
Using the product to sum of logarithm given by the formula
Rearranging the terms we can write the above expression as: -
Using the algebraic identity: -
Taking (-1) common in the L.H.S., we have,
Cancelling the common factors on both the sides, we get,
Using the formula
Now, we can see that the base of the logarithm on both sides are the same, so we can equate their arguments by removing the log function. Therefore, we have,
Hence, option (c) is our answer.
Note: One may note that it will be difficult for us to solve the question in the exponential form and that is why we took the help of log to solve the question. The reason for taking log to the base ‘b’ was that we can clearly see that we had
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
What are Quantum numbers Explain the quantum number class 11 chemistry CBSE

Write the differences between monocot plants and dicot class 11 biology CBSE

In northern hemisphere 21st March is called as A Vernal class 11 social science CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

List out the uses of ethanoic acid class 11 chemistry CBSE

Number of oneone functions from A to B where nA 4 and class 11 maths CBSE
