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 (7^{x}) + 343 = 0

x = 2, x = 1

Solution steps

7^{2 x} - 56 (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

3^{2 x} = 1000

4 9^{x} - 6 \cdot 7^{x} + 5 = 0

t, e^{t^{2}} = 4

5^{x + 2} = 5^{2 x - 1}

\frac{2 ^{3 x - 1}}{2 ^{x + 5}} = 2^{x}

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