Question

সমাধান কর: $\left(\sqrt3\right)^{x+1}=\left(\sqrt[3]{3}\right)^{2x-1}$

Answer 1

$\left(\sqrt3\right)^{x+1}=\left(\sqrt[3]{3}\right)^{2x-1}$

বা, $\left(3^{\frac12}\right)^{x+1}=\left(3^{\frac13}\right)^{2x-1}$

বা, $3^{\frac{x+1}{2}}=3^{\frac{2x-1}{3}}$

বা, $\frac{x+1}{2}=\frac{2x-1}{3}$

বা, $2\left(2x-1\right)=3\left(x+1\right)$

বা, $4x-2=3x+3$

বা, $4x-3x=3+2$

$\therefore x=5$ [Answer]

Comments

Rules Applied:

• $\left(a^{m}\right)^{n}=a^{mn}$
• $a^x=a^y\Rightarrow x=y$