Power, Indices and Surds MCQ Question with Answer

Solution: $4^{2x}-2^{2x}=12$

$\Rightarrow 2^{4x}-2^{2x}=12, Let\,\,2^{2x\,\,}=a$

$\therefore a^2-a-12=0$

$\Rightarrow \left( a-4 \right) \left( a+3 \right) =0$

$\therefore a=\,\,4 or\,\,a=-3; if\,\,a=-3 then\,\,it\,\,complex\,\,number$

$\therefore a=4$

$\Rightarrow 2^{2x}=2^2$

$\Rightarrow x=1$

Solution: $9^x-10.3^x+9=0$

$\Rightarrow 3^{2x}-10.3^x+9=0, Let\,\,3^x=a$

$\Rightarrow a^2-10a+9=0$

$\Rightarrow \left( a-9 \right) \left( a-1 \right) =0$

$\therefore a=9 or\,\,a=1$

$\Rightarrow 3^x=3^2\,\,or\,\,3^x=3^0$

$\Rightarrow x=2 or\,\,0$

Solution: $\sqrt[3]{x^{12}}+\sqrt{x^6}=x^{\frac{12}{3}}+x^{\frac{6}{2}}=\,\,x^4+x^3$