Discussion
If \(\left(\frac{5}{7}\right)^{4} \times \left(\frac{5}{7}\right)^{-3}\) \(= \left(\frac{5}{7}\right)^{5x-2}\), then x is
Answer: C
The value of x is 3/5.
With the same base, multiplying powers means adding the exponents:
\[ \begin{aligned} \left(\tfrac{5}{7}\right)^{4} \times \left(\tfrac{5}{7}\right)^{-3} &= \left(\tfrac{5}{7}\right)^{1} \\ 5x - 2 &= 1 \\ x &= \tfrac{3}{5} \end{aligned} \]
1/5 comes from solving 5x − 2 = −1 (subtracting the exponents the wrong way), and the other values do not satisfy the equation.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development