JEE Mains · Maths · STD 12 - 1. relation and function
The inverse of \(y=5^{\log x}\) is
- A \(x =5^{\text {logy }}\)
- B \(x=y^{\log 5}\)
- C \(x = y ^{\frac{1}{\log 5}}\)
- D \(x =5^{\frac{1}{\log y}}\)
Answer & Solution
Correct Answer
(C) \(x = y ^{\frac{1}{\log 5}}\)
Step-by-step Solution
Detailed explanation
Given \(y=5^{\left(\log _{a} x\right)}=f(x)\) Interchanging \(x \& y\) for inverse \(x=5^{\left(\log _{a} y\right)}=y^{\left(\log _{a} 5\right)}\) option \((1)\) or option \((2)\) Further, from given relation \(\log _{5} y =\log _{ a } x\)…
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