Solve for x
x=y
Solve for y
y=x
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2017^{x-y}=1
Use the rules of exponents and logarithms to solve the equation.
\log(2017^{x-y})=\log(1)
Take the logarithm of both sides of the equation.
\left(x-y\right)\log(2017)=\log(1)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x-y=\frac{\log(1)}{\log(2017)}
Divide both sides by \log(2017).
x-y=\log_{2017}\left(1\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=-\left(-y\right)
Subtract -y from both sides of the equation.
2017^{-y+x}=1
Use the rules of exponents and logarithms to solve the equation.
\log(2017^{-y+x})=\log(1)
Take the logarithm of both sides of the equation.
\left(-y+x\right)\log(2017)=\log(1)
The logarithm of a number raised to a power is the power times the logarithm of the number.
-y+x=\frac{\log(1)}{\log(2017)}
Divide both sides by \log(2017).
-y+x=\log_{2017}\left(1\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
-y=-x
Subtract x from both sides of the equation.
y=-\frac{x}{-1}
Divide both sides by -1.
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Simultaneous equation
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Differentiation
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Integration
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Limits
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