What is the answer to 5^x+5^{5-x}=150 ?

The answer to 5^x+5^{5-x}=150 is x=3,x=2

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5^x+5^{5-x}=150

5^{x} + 5^{5 - x} = 150

x = 3, x = 2

Solution steps

5^{x} + 5^{5 - x} = 150

Apply exponent rules

5^{x} + (5^{x})^{- 1} \cdot 5^{5} = 150

Rewrite the equation with

5^{x} = u

u + (u)^{- 1} \cdot 5^{5} = 150

Solve

u + u^{- 1} \cdot 5^{5} = 150 : u = 125, u = 25

u = 125, u = 25

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 125 : x = 3

Solve

5^{x} = 25 : x = 2

x = 3, x = 2

20.0855 = e^{x}

7^{x} = 343

7^{x - 1} = e

\frac{1}{3} = 3^{2 x + 2}

e^{2 x} = 2

What is the answer to 5^x+5^{5-x}=150 ?
The answer to 5^x+5^{5-x}=150 is x=3,x=2
Solve for x: 5^x+5^{5-x}=150
The solution is x=3,x=2