What is the answer to 6-5^x=5^{1-x} ?

The answer to 6-5^x=5^{1-x} is x=0,x=1

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6-5^x=5^{1-x}

6 - 5^{x} = 5^{1 - x}

x = 0, x = 1

Solution steps

6 - 5^{x} = 5^{1 - x}

Apply exponent rules

6 - 5^{x} = (5^{x})^{- 1} \cdot 5^{1}

Rewrite the equation with

5^{x} = u

6 - u = (u)^{- 1} \cdot 5^{1}

Solve

6 - u = u^{- 1} \cdot 5^{1} : u = 1, u = 5

u = 1, u = 5

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 1 : x = 0

Solve

5^{x} = 5 : x = 1

x = 0, x = 1

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2.95 = 2.33 e^{2 c}

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e^{2 x} - 11 e^{x} + 30 = 0