Question 125

$$(\sqrt{3})^{5}\times 9^{2}=3^{n}\times3\sqrt{3}$$ then find the value of n

Solution

$$(\sqrt{3})^{5}\times 9^{2}=3^{n}\times3\sqrt{3}$$

$$(3)^\frac{5}{2}\times 3^{4}=3^{n}\times(3)^{\frac{3}{2}}$$

$$(3)^\frac{13}{2}=3^{n}\times(3)^{\frac{3}{2}}$$

$$(3)^\frac{10}{2}=3^{n}$$

$$n=5$$

so the answer is option A.

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