Answer
Verified
480.3k+ views
Hint: We are going to simplify the given expression using basic logarithmic formulae.
Given expression is $${\log _b}x \cdot {\log _a}b$$
Using the change of base rule from logarithms, we can write the above expression as
$ = \frac{{\log x}}{{\log b}} \times \frac{{\log b}}{{\log a}}$
On simplifying this we get
$ = \frac{{\log x}}{{\log a}}$
$ = {\log _a}x$
Note:
We simplified the given expression using change of base rule of logarithms. That is
${\log _b}a = \frac{{{{\log }_x}a}}{{{{\log }_x}b}}$
This formula allows us to rewrite the logarithm in terms of logarithms written in another base.
Given expression is $${\log _b}x \cdot {\log _a}b$$
Using the change of base rule from logarithms, we can write the above expression as
$ = \frac{{\log x}}{{\log b}} \times \frac{{\log b}}{{\log a}}$
On simplifying this we get
$ = \frac{{\log x}}{{\log a}}$
$ = {\log _a}x$
Note:
We simplified the given expression using change of base rule of logarithms. That is
${\log _b}a = \frac{{{{\log }_x}a}}{{{{\log }_x}b}}$
This formula allows us to rewrite the logarithm in terms of logarithms written in another base.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE