Question

How to solve this plss frac{(\sqrt{(3)})^{5}}{((\sqrt{(3)})^{-4})}=(\sqrt{(3)})^{(2k+1)​

Answer 1

k = 4

Explanation:

Given equation:

`((√(3))^(5))/((√(3))^(-4))=(√(3))^((2k+1))`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies (√(3))^((5-(-4)))=(√(3))^((2k+1))`

`\implies (√(3))^(9)=(√(3))^((2k+1))`

`\textsf{Apply exponent rule} \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x):`

`\implies (√(3))^(9)=(√(3))^((2k+1))`

`\implies 9=2k+1`

`\implies 2k=8`

`\implies k=4`