If 9^ 1+ x =3^ 1+ x +210 (where base of is 3 ) then integral value of x is:

Correct answer: 5 aligned 3^ 2+2 _3 x & =3^ 1+ _3 x +210 9 x^2 & =3 x+210 9 x^2-3 x-210 & =0 x=5 aligned

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JEE Advanced · Mathematics · Basics of Mathematics

If 9^ 1+ x =3^ 1+ x +210 (where base of is 3 ) then integral value...

9^{1+\log x}=3^{1+\log x}+210

(where base of

\log

is 3 ) then integral value of

x

is:

\begin{aligned} 3^{2+2 \log _3 x} & =3^{1+\log _3 x}+210 \\ 9 x^2 & =3 x+210 \\ \Rightarrow \quad 9 x^2-3 x-210 & =0 \Rightarrow x=5\end{aligned}