What is the answer to 6^{2x}-42(6^x)+216=0 ?

The answer to 6^{2x}-42(6^x)+216=0 is x=2,x=1

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6^{2x}-42(6^x)+216=0

6^{2 x} - 42 (6^{x}) + 216 = 0

x = 2, x = 1

Solution steps

6^{2 x} - 42 (6^{x}) + 216 = 0

Apply exponent rules

(6^{x})^{2} - 42 \cdot 6^{x} + 216 = 0

Rewrite the equation with

6^{x} = u

(u)^{2} - 42 u + 216 = 0

Solve

u^{2} - 42 u + 216 = 0 : u = 36, u = 6

u = 36, u = 6

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 36 : x = 2

Solve

6^{x} = 6 : x = 1

x = 2, x = 1

y, e^{x^{2} y} = x + y

10 = 0.1 7^{- x}

2^{x - 2} = 5

5^{100} - 5^{99} = 4 \cdot 5^{x}

2 = c e^{- t} + \frac{1}{2 e ^{t}}

What is the answer to 6^{2x}-42(6^x)+216=0 ?
The answer to 6^{2x}-42(6^x)+216=0 is x=2,x=1
Solve for x: 6^{2x}-42(6^x)+216=0
The solution is x=2,x=1