5^x*3^y=135 3^y-5^x+1=2

$$3^{y} 5^{x} = 135$$

y x
3 – 5 + 1 = 2

$$3^{y} – 5^{x} + 1 = 2$$

$$x_{1} = frac{1}{log{left (5 right )}} left(- log{left (1 + sqrt{541} right )} + log{left (270 right )}right)$$
=
$$frac{1}{log{left (5 right )}} left(- log{left (1 + sqrt{541} right )} + log{left (270 right )}right)$$
=

1.49717953895072

$$y_{1} = frac{1}{log{left (3 right )}} left(- log{left (2 right )} + log{left (1 + sqrt{541} right )}right)$$
=
$$frac{1}{log{left (3 right )}} left(- log{left (2 right )} + log{left (1 + sqrt{541} right )}right)$$
=

2.27164514039444

$$x_{2} = frac{1}{log{left (5 right )}} left(log{left (- frac{270}{- sqrt{541} + 1} right )} + i piright)$$
=
$$frac{1}{log{left (5 right )}} left(log{left (- frac{270}{- sqrt{541} + 1} right )} + i piright)$$
=

1.55063904450723 + 1.95198126583117*i

$$y_{2} = frac{1}{log{left (3 right )}} left(log{left (- frac{1}{2} + frac{sqrt{541}}{2} right )} + i piright)$$
=
$$frac{1}{log{left (3 right )}} left(log{left (- frac{1}{2} + frac{sqrt{541}}{2} right )} + i piright)$$
=

2.19332838032348 + 2.85960086738013*i

x1 = 1.497179538950724
y1 = 2.271645140394442