Solve` log_(2)(25^(x+3)-1) = 2 + log_(2)(5^(x+3) + 1)`.

Answer

x = - 2

Explanation

`log_(2)(25^(x+3)-1)=2+log_(2)(5^(x+3)+1)`
` or log_(2) (25^(x+3)-1)-log_(2)(5^(x+3)+1) = 2`
` or log_(2). (25^(x+3)-1)/(5^(x+3)+1) = 2`
`or (25^(x+3)-1)/(5^(x+3)+1) = 2^(2)`
` or y^(2) - 1 = 4y + 4" "("putting "5^(x+3)=y)`
` or y^(2) -4y-5 = 0`
` or y =-1, 5`
` rArr 5^(x+3) = 5 `
` or x =- 2`