All Categories
Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
If a^x = b^y and a = b^k, what is the relationship between x, y, and k?
If a^x = b^y and a = b^k, what is the relationship between x, y, and k?
Expand All
Collapse All
Practice Questions
1 question
Q1
If a^x = b^y and a = b^k, what is the relationship between x, y, and k?
x = ky
y = kx
x + y = k
x - y = k
Show Solution
Copy
Substituting a = b^k into a^x = b^y gives (b^k)^x = b^y, leading to kx = y, hence x = ky.
Questions & Step-by-step Solutions
1 item
Q
Q: If a^x = b^y and a = b^k, what is the relationship between x, y, and k?
Solution:
Substituting a = b^k into a^x = b^y gives (b^k)^x = b^y, leading to kx = y, hence x = ky.
Steps: 7
Show Steps
Step 1: Start with the equation a^x = b^y.
Step 2: We know that a = b^k. Substitute b^k for a in the equation.
Step 3: This gives us (b^k)^x = b^y.
Step 4: Use the power of a power rule: (b^k)^x can be rewritten as b^(kx).
Step 5: Now we have b^(kx) = b^y.
Step 6: Since the bases (b) are the same, we can set the exponents equal to each other: kx = y.
Step 7: To find the relationship between x, y, and k, we can rearrange this equation to get x = y/k.
Related Questions
W
What is the wavelength of a photon with a frequency of 6 x 10^14 Hz?
Question: What is the wavelength of a photon with a frequency of 6 x 10^14 Hz?Options: 5 x 10^-7 m3 ..
F
Find the value of tan(45°).
Question: Find the value of tan(45°).Options: 01undefined√3Correct Answer: 1Solution: tan(45°) = 1...
W
What is the value of 5C2?
Question: What is the value of 5C2?Options: 1020155Correct Answer: 10Solution: 5C2 = 5! / (2!(5-2)!)..
W
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
Question: What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?Options: 3x^2 - 6x + 43x^2 - 6x2x^2 -..
A
A 10 kg object is moving with a speed of 3 m/s. If it comes to a stop, how much
Question: A 10 kg object is moving with a speed of 3 m/s. If it comes to a stop, how much work is do..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
