Find the value of \(\frac{5 x+1}{3}\), if \(25^{4 x-3}=5^{6 x+8}\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12
Write both sides as powers of the same base, 5. When two powers of the same base are equal, their exponents are equal, which gives an equation in \(x\).
Left side as a power of 5: \(25^{4x-3}=(5^{2})^{4x-3}=5^{8x-6}\)
Equating the exponents: \(8x-6=6x+8\)
\(2x=14\), so \(x=7\)
Required value: \(\displaystyle \frac{5x+1}{3}=\frac{35+1}{3}=12\)