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.
$5^x\times3^y=45$
$3^x\times5^y=75$
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2$\begingroup$ Multiply the two euqtions: You get a value for $x+y$. Divide the two equations, you get a value for $x-y$ $\endgroup$– voldemortJan 22, 2015 at 1:09
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$\begingroup$ What should I multiply with to get the value of $x+y$? $\endgroup$– Nouvel RakaJan 22, 2015 at 5:58
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$\begingroup$ Multiply the first equation to the second equation. $\endgroup$– velut lunaJan 22, 2015 at 6:11
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$\begingroup$ Super thank you voldemort and @kyson, I found the solution. I got $x=1$ and $y=2$. $\endgroup$– Nouvel RakaJan 23, 2015 at 1:29
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1 Answer
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Take log.
$$x\log5+y\log3=\log45$$
$$x\log3+y\log5=\log75$$
answered Jan 22, 2015 at 1:15
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$\begingroup$ 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. $\endgroup$ Jan 22, 2015 at 4:12
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$\begingroup$ Do you know how to solve simultaneous linear equations? Otherwise, you can follow voldmort's method. $\endgroup$ Jan 22, 2015 at 5:40
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$\begingroup$ I know how to solve simultaneous linear equations. But I don't know how to modify these equations as they have logarithm in it. And, what is voldmort's method? $\endgroup$ Jan 22, 2015 at 5:55
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$\begingroup$ The method suggested by voldmort in his comment on your post. $\endgroup$ Jan 22, 2015 at 6:04
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$\begingroup$ If you know how to simultaneous linear equations, then you should be able to solve the equations in the answer I posted. It's just two simultaneous linear equations. The coefficients are logarithms though. But logarithms are just numbers. $\endgroup$ Jan 22, 2015 at 6:06