What is the answer to 36(6^{2x})-217(6^x)+6=0 ?

The answer to 36(6^{2x})-217(6^x)+6=0 is x=1,x=-2

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36(6^{2x})-217(6^x)+6=0

36 (6^{2 x}) - 217 (6^{x}) + 6 = 0

x = 1, x = - 2

Solution steps

36 (6^{2 x}) - 217 (6^{x}) + 6 = 0

Apply exponent rules

36 (6^{x})^{2} - 217 \cdot 6^{x} + 6 = 0

Rewrite the equation with

6^{x} = u

36 (u)^{2} - 217 u + 6 = 0

Solve

36 u^{2} - 217 u + 6 = 0 : u = 6, u = \frac{1}{36}

u = 6, u = \frac{1}{36}

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 6 : x = 1

Solve

6^{x} = \frac{1}{36} : x = - 2

x = 1, x = - 2

4^{- x} = \frac{1}{256}

e^{x} = 4 - x

(\frac{2}{3})^{x} = \frac{8}{27}

x^{x} = 2^{\frac{1}{6}}

73 = 1 5^{x}

What is the answer to 36(6^{2x})-217(6^x)+6=0 ?
The answer to 36(6^{2x})-217(6^x)+6=0 is x=1,x=-2
Solve for x: 36(6^{2x})-217(6^x)+6=0
The solution is x=1,x=-2