# What's the solution to this exponential system of equation?

What are the steps to solving a system of equations when $x$ and $y$ are exponents? But they have different base. Here is the problem.

$5^x\times3^y=45$

$3^x\times5^y=75$

• Multiply the two euqtions: You get a value for $x+y$. Divide the two equations, you get a value for $x-y$ Jan 22, 2015 at 1:09
• What should I multiply with to get the value of $x+y$? Jan 22, 2015 at 5:58
• Multiply the first equation to the second equation. Jan 22, 2015 at 6:11
• Super thank you voldemort and @kyson, I found the solution. I got $x=1$ and $y=2$. Jan 23, 2015 at 1:29

$$x\log5+y\log3=\log45$$
$$x\log3+y\log5=\log75$$
• I'm sorry, I'm still confuse how to find the value of $x$ and $y$. Since the $x$ and $y$ are the power for different number, I can't manipulate them. And after taking logarithm, though, it couldn't help me yet. Jan 22, 2015 at 4:12