What is the answer to 7^{2x}-56*7^x+343=0 ?

The answer to 7^{2x}-56*7^x+343=0 is x=2,x=1

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7^{2x}-56*7^x+343=0

7^{2 x} - 56 \cdot 7^{x} + 343 = 0

x = 2, x = 1

Solution steps

7^{2 x} - 56 \cdot 7^{x} + 343 = 0

Apply exponent rules

(7^{x})^{2} - 56 \cdot 7^{x} + 343 = 0

Rewrite the equation with

7^{x} = u

(u)^{2} - 56 u + 343 = 0

Solve

u^{2} - 56 u + 343 = 0 : u = 49, u = 7

u = 49, u = 7

Substitute back

u = 7^{x},

solve for

x

Solve

7^{x} = 49 : x = 2

Solve

7^{x} = 7 : x = 1

x = 2, x = 1

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What is the answer to 7^{2x}-56*7^x+343=0 ?
The answer to 7^{2x}-56*7^x+343=0 is x=2,x=1
Solve for x: 7^{2x}-56*7^x+343=0
The solution is x=2,x=1