Calculate: x+1=log_{(3)/(5)}((125)/(27))

Expression: $x+1=\log_{ \frac{ 3 }{ 5 } }({ \frac{ 125 }{ 27 } })$

Write the number in exponential form with the base of $\frac{ 3 }{ 5 }$

$x+1=\log_{ \frac{ 3 }{ 5 } }({ {\left( \frac{ 3 }{ 5 } \right)}^{-3} })$

Use $\log_{ a }({ {a}^{x} })=x$ to simplify the expression

$x+1=-3$

Move the constant to the right-hand side and change its sign

$x=-3-1$

Calculate the difference

$x=-4$