Question

243 = √3 (√3) ^n-1
find value of n ?​

Answer 1

Answer:

243=3^n-1

3^5=3^n-1

5=n-1

n=6

Answer 2

Answer:

n = 10

Step-by-step explanation:

$243 = \sqrt{3} ( { \sqrt{3} \: )}^{n - 1} \\ \\ \sqrt{x} = {x}^{ \frac{1}{2} } \\ \\ \\ {3}^{5} = ({3})^{ \frac{1}{2} } ( {3})^{ \frac{n - 1}{2} } \\ \\ \\ {x}^{m} \times {x}^{n} = {x}^{m + n} \\ \\ \\ {3}^{5} = {3}^{ (\frac{1}{2} + \frac{n - 1}{2} )} \\ \\ {3}^{5} = {3}^{ (\frac{1 + n - 1}{2}) } \\ \\ {3}^{5} = {3}^{( \frac{n}{2} )} \\ \\ {x}^{m} = {x}^{n} =>> m = n \\ \\ 5 = \frac{n}{2} \\ \\ n = 5 \times 2 \\ n = 10$