What is the answer to 5^x+125(5^{-x})=30 ?

The answer to 5^x+125(5^{-x})=30 is x=2,x=1

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5^x+125(5^{-x})=30

5^{x} + 125 (5^{- x}) = 30

x = 2, x = 1

Solution steps

5^{x} + 125 (5^{- x}) = 30

Apply exponent rules

5^{x} + 125 (5^{x})^{- 1} = 30

Rewrite the equation with

5^{x} = u

u + 125 (u)^{- 1} = 30

Solve

u + 125 u^{- 1} = 30 : u = 25, u = 5

u = 25, u = 5

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = 5 : x = 1

x = 2, x = 1

3^{x} = 7^{x + 2}

2^{x - 3} + 2^{x - 1} + 2^{x} = 52

3 6^{x} + 4 2^{x} = 4 9^{x}

5 \cdot 1 8^{6 x} = 26

5^{x} = 4

What is the answer to 5^x+125(5^{-x})=30 ?
The answer to 5^x+125(5^{-x})=30 is x=2,x=1
Solve for x: 5^x+125(5^{-x})=30
The solution is x=2,x=1