What is the answer to 11*10^{x-3}-10^{2x-4}=0.1 ?

The answer to 11*10^{x-3}-10^{2x-4}=0.1 is x=1,x=2

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11*10^{x-3}-10^{2x-4}=0.1

11 \cdot 1 0^{x - 3} - 1 0^{2 x - 4} = 0.1

x = 1, x = 2

Solution steps

11 \cdot 1 0^{x - 3} - 1 0^{2 x - 4} = 0.1

Apply exponent rules

11 \cdot 1 0^{x} \cdot 1 0^{- 3} - (1 0^{x})^{2} \cdot 1 0^{- 4} = 0.1

Rewrite the equation with

1 0^{x} = u

11 u \cdot 1 0^{- 3} - (u)^{2} \cdot 1 0^{- 4} = 0.1

Solve

11 u \cdot 1 0^{- 3} - u^{2} \cdot 1 0^{- 4} = 0.1 : u = 10, u = 100

u = 10, u = 100

Substitute back

u = 1 0^{x},

solve for

x

Solve

1 0^{x} = 10 : x = 1

Solve

1 0^{x} = 100 : x = 2

x = 1, x = 2

5^{2 x} 3 = 75

x e^{x} - 7 x e^{x} = 0

1 0^{x} = 41000

5^{1 - 2 x} = 3

3^{2 x} + 3^{x + 1} - 10 = 0

What is the answer to 11*10^{x-3}-10^{2x-4}=0.1 ?
The answer to 11*10^{x-3}-10^{2x-4}=0.1 is x=1,x=2
Solve for x: 11*10^{x-3}-10^{2x-4}=0.1
The solution is x=1,x=2