Q90 / 180 · COMEDK 2012 · Mathematics
If $4^{\log _{9} 3}+9^{\log _{2} 4}=10^{\log _{x} 83}$, then $x$ is equal to
- Correct answerA10
- B4
- C$-10$
- D$-4$
Solution
We have,
$4^{\log _{9}} 3+9^{\log _{2}} 4=10^{\log _{x} 83}$
$\Rightarrow 4^{\frac{1}{2} \log _{3}} 3+9^{2 \log _{2}} 2=10^{\log _{x}} 83$
$\Rightarrow \quad 2+81=10^{\log _{x}} 83$
$\Rightarrow \quad 83=10^{\log _{x}} 83$
$\Rightarrow \quad \log _{10} 83=\log _{x} 83$
$\Rightarrow \quad x=10$
Hence, the correct answer is option: 'A'.