LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
7 views
in Sets, Relations and Functions by (54.3k points)
closed by
Find the value of x if \(25^{log_{5}25}-9^{log_{81}9}=7^{log_{7}x}\)
5. 81

1 Answer

0 votes
by (30.0k points)
selected by
 
Best answer
Correct Answer - Option 2 : 622

Concept:

  • \(a^{log_{b}a}=\sqrt{a}\), If b = a2, a > 0, b > 0, b \( \neq\) 1.
  • \(a^{log_{b}a}=a^2\), If a = b2, a > 0, b > 0, b \( \neq\) 1

Calculation:

Given:  \(25^{log_{5}25}-9^{log_{81}9}=7^{log_{7}x}\)

By using the properties mentioned in the concept part we get

⇒ \(25^2-\sqrt9=7^{log_{7}x}\)

⇒ \(625-3=7^{log_{7}x}\)

⇒ \(622=7^{log_{7}x}\)

By taking log on both sides to the base 7 we get

⇒ \({log_{7}622}={log_{7}x} \times {log_{7}7}\)

⇒ \({log_{7}622}={log_{7}x}\)

By comparing LHS and RHS, we get x = 622

Hence, option 2 is correct.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...