What is the answer to 6(6^{2x})-37(6^x)+6=0 ?

The answer to 6(6^{2x})-37(6^x)+6=0 is x=1,x=-1

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6(6^{2x})-37(6^x)+6=0

6 (6^{2 x}) - 37 (6^{x}) + 6 = 0

x = 1, x = - 1

Solution steps

6 (6^{2 x}) - 37 (6^{x}) + 6 = 0

Apply exponent rules

(6^{x})^{2} \cdot 6^{1} - 37 \cdot 6^{x} + 6 = 0

Rewrite the equation with

6^{x} = u

(u)^{2} \cdot 6^{1} - 37 u + 6 = 0

Solve

u^{2} \cdot 6^{1} - 37 u + 6 = 0 : u = 6, u = \frac{1}{6}

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

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 6 : x = 1

Solve

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

x = 1, x = - 1

e^{2 x} = 3 e^{x}

10 \cdot 3^{\frac{5 t}{4}} = 800

1^{x} = - 1

- 15 \cdot 2^{- 0.5 x} = - 90

4 \cdot 2^{5 x} = 21

What is the answer to 6(6^{2x})-37(6^x)+6=0 ?
The answer to 6(6^{2x})-37(6^x)+6=0 is x=1,x=-1
Solve for x: 6(6^{2x})-37(6^x)+6=0
The solution is x=1,x=-1