Q51 / 170 · Manipal (MET) 2018 · Mathematics
The equation $3^{|3 x+4|}=9^{2 x-2}, x\gt0$ has the solution
- A$\frac{7}{8}$
- B$\frac{8}{7}$
- C$\frac{-3}{4}$
- Correct answerDNone of these
Solution
$3^{|3 x+4|}=9^{2 x-2}, x\gt0$
When $x\gt0$, then $\begin{aligned} & & |3 x+4| & =3 x+4 \\ \therefore & & 3^{3 x+4} & =3^{2(2 x-2)} \\ \Rightarrow & & 3 \hat{x}+4 & =4 \dot{x}-4 \\ \Rightarrow & & x & =8 \end{aligned}$
When $x\gt0$, then $\begin{aligned} & & |3 x+4| & =3 x+4 \\ \therefore & & 3^{3 x+4} & =3^{2(2 x-2)} \\ \Rightarrow & & 3 \hat{x}+4 & =4 \dot{x}-4 \\ \Rightarrow & & x & =8 \end{aligned}$
Hence, the correct answer is option: 'D'.