What is the answer to 9^x-3^x-2=0 ?

The answer to 9^x-3^x-2=0 is x=(ln(2))/(ln(3))

Solve for x: 9^x-3^x-2=0

The solution is x=(ln(2))/(ln(3))

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9^{x} - 3^{x} - 2 = 0

x = \frac{ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = 0.63092 \dots

Solution steps

9^{x} - 3^{x} - 2 = 0

Apply exponent rules

(3^{x})^{2} - 3^{x} - 2 = 0

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} - u - 2 = 0 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 2 : x = \frac{ln ( 2 )}{ln ( 3 )}

Solve

3^{x} = - 1 :

No Solution for

x \in R

x = \frac{ln ( 2 )}{ln ( 3 )}

e^{x} + x - 2 = 0

3^{1 - x} = 2

2^{4 x} = 16

2^{x} - 3^{x} - 3^{x} = 0

4 (10)^{x} = 20

What is the answer to 9^x-3^x-2=0 ?
The answer to 9^x-3^x-2=0 is x=(ln(2))/(ln(3))
Solve for x: 9^x-3^x-2=0
The solution is x=(ln(2))/(ln(3))