Solve for x

x=\frac{x_{2}+6}{5}

Solve for x_2

x_{2}=5x-6

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5^{-5x+x_{2}+6}=1

Use the rules of exponents and logarithms to solve the equation.

\log(5^{-5x+x_{2}+6})=\log(1)

Take the logarithm of both sides of the equation.

\left(-5x+x_{2}+6\right)\log(5)=\log(1)

The logarithm of a number raised to a power is the power times the logarithm of the number.

-5x+x_{2}+6=\frac{\log(1)}{\log(5)}

Divide both sides by \log(5).

-5x+x_{2}+6=\log_{5}\left(1\right)

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

-5x=-\left(x_{2}+6\right)

Subtract x_{2}+6 from both sides of the equation.

x=-\frac{x_{2}+6}{-5}

Divide both sides by -5.

5^{x_{2}+6-5x}=1

Use the rules of exponents and logarithms to solve the equation.

\log(5^{x_{2}+6-5x})=\log(1)

Take the logarithm of both sides of the equation.

\left(x_{2}+6-5x\right)\log(5)=\log(1)

The logarithm of a number raised to a power is the power times the logarithm of the number.

x_{2}+6-5x=\frac{\log(1)}{\log(5)}

Divide both sides by \log(5).

x_{2}+6-5x=\log_{5}\left(1\right)

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

x_{2}=-\left(6-5x\right)

Subtract -5x+6 from both sides of the equation.

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