What is the answer to 6^{2x}+6^x-12=0 ?

The answer to 6^{2x}+6^x-12=0 is x=(ln(3))/(ln(6))

Solve for x: 6^{2x}+6^x-12=0

The solution is x=(ln(3))/(ln(6))

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6^{2 x} + 6^{x} - 12 = 0

x = \frac{ln ( 3 )}{ln ( 6 )}

Decimal Notation

x = 0.61314 \dots

Solution steps

6^{2 x} + 6^{x} - 12 = 0

Apply exponent rules

(6^{x})^{2} + 6^{x} - 12 = 0

Rewrite the equation with

6^{x} = u

(u)^{2} + u - 12 = 0

Solve

u^{2} + u - 12 = 0 : u = 3, u = - 4

u = 3, u = - 4

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 6 )}

Solve

6^{x} = - 4 :

No Solution for

x \in R

x = \frac{ln ( 3 )}{ln ( 6 )}

500 e^{- 2 x} = 125

2^{x + 1} + 2^{x} = 24

a, s^{b} r^{a} = r^{- a} s^{b}

3^{x} = 34

e^{x + 1} = 8^{x + 8}

What is the answer to 6^{2x}+6^x-12=0 ?
The answer to 6^{2x}+6^x-12=0 is x=(ln(3))/(ln(6))
Solve for x: 6^{2x}+6^x-12=0
The solution is x=(ln(3))/(ln(6))