Question 77
If $$\left(\sqrt{\frac{3}{5}}\right)^a = \left(\sqrt{\frac{625}{81}}\right)^{\frac{a + 3}{2}}$$, then a =
Solution
The RHS of the equation can be modified as $$\left(\sqrt{\ \frac{81}{625}}\right)^{-\frac{\left(a+3\right)}{2}}=\left(\sqrt{\ \frac{3}{5}}\right)^{4\cdot\left(-\frac{\left(a+3\right)}{2}\right)}$$
As the bases are equal on both sides, respective powers can be equated:
a = -2*(a+3)
a = -2
Get AI Help
Create a FREE account and get:
- Download Maths Shortcuts PDF
- Get 300+ previous papers with solutions PDF
- 500+ Online Tests for Free
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Session:Free CAT Mentorship
Phone:
Date:
Time:
Enter OTP
Didn't receive the OTP?
