Alerts Wishlist Cart

If log_5(25) = x, what is the value of log_5(5^x)?

Practice Questions

Q1
If log_5(25) = x, what is the value of log_5(5^x)?
  1. x
  2. 2x
  3. x^2
  4. 5x

Questions & Step-by-Step Solutions

If log_5(25) = x, what is the value of log_5(5^x)?
Correct Answer: x
  • Step 1: Understand that log_5(25) = x means that 5 raised to the power of x equals 25.
  • Step 2: Rewrite 25 as 5^2. So, we have 5^x = 5^2.
  • Step 3: Since the bases are the same (both are 5), we can set the exponents equal to each other: x = 2.
  • Step 4: Now, we need to find log_5(5^x). Substitute x with 2: log_5(5^2).
  • Step 5: Use the property of logarithms that says log_b(b^y) = y. Here, b is 5 and y is 2.
  • Step 6: Therefore, log_5(5^2) = 2.
  • Logarithmic Properties – Understanding the properties of logarithms, particularly that log_b(b^a) = a.
  • Change of Base – Recognizing how to manipulate logarithmic expressions using known values.
Biology (School & UG)
Biology (School & UG)
Chemistry (School & UG)
Chemistry (School & UG)
Civil Engineering
Civil Engineering
Commerce & Accountancy
Commerce & Accountancy
Computer Science & IT
Computer Science & IT
Current Affairs & GK
Current Affairs & GK
Data Structures & Algorithms
Data Structures & Algorithms
eBooks
eBooks
Electrical & Electronics Engineering
Electrical & Electronics Engineering
English (School)
English (School)
General Aptitude
General Aptitude
General Knowledge
General Knowledge
General Knowledge & Current Affairs
General Knowledge & Current Affairs
Languages & Literature
Languages & Literature
Law & Legal Studies
Law & Legal Studies
Major Competitive Exams
Major Competitive Exams
Mathematics (School)
Mathematics (School)
Mechanical Engineering
Mechanical Engineering
Medical Science
Medical Science
Physics (School & Undergraduate)
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Quantitative Aptitude & Reasoning
Social Science (School)
Social Science (School)
Technical
Technical
Verbal and Reasoning
Verbal and Reasoning
Vocational & Skill Development
Vocational & Skill Development
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely