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$125\left(\sqrt5\right)^{2x}=1$ হলে $x$ এর মান কত?

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$125\left(\sqrt5\right)^{2x}=1$ হলে $x$ এর মান কত?

Options :

  • (A) $3$
  • (B) $-3$
  • (C) $7$
  • (D) $9$

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$125\left(\sqrt5\right)^{2x}=1$

বা, $125 \times 5^{\frac{1}{2} \times 2x}=1$ [ $\because \sqrt a = a^{\frac12}$ ]

বা, $125 \times 5^x=1$

বা, $5^3 \times 5^x=1$

বা, $5^{3+x}=5^0$

বা, $3+x=0$

$\therefore$ $x=-3$

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