Find the value of `x` in each of the following: `(i)\ 5^(2x+3)=1` `(ii)\ (13)^(sqrt(x))=4^4-3^4-6` `(iii)\ (sqrt(3/5))^(x+1)=(125)/(27)`

Explanation

`(i)5^(2x+3)=1`

`5^(2x+3)=5^0`

we have `2x+3=0`
so x`=(-3/2)`

`(ii)(13)^(sqrt(x))=4^4-3^4-6`
`(13)^(sqrt(x))=169`
`(13)^(sqrt(x))=13^2`
`sqrt(x)=2` so `x=4`

(iii) `(sqrt(3/5))^(x+1)=(125)/(27)`
`(sqrt(5/3))^-(x+1)=(5/3)^3`
on comparing both side `x=-7`