What is the answer to 9^x-6*3^x-55=0 ?

The answer to 9^x-6*3^x-55=0 is x=(ln(11))/(ln(3))

Solve for x: 9^x-6*3^x-55=0

The solution is x=(ln(11))/(ln(3))

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9^{x} - 6 \cdot 3^{x} - 55 = 0

x = \frac{ln ( 11 )}{ln ( 3 )}

Decimal Notation

x = 2.18265 \dots

Solution steps

9^{x} - 6 \cdot 3^{x} - 55 = 0

Apply exponent rules

(3^{x})^{2} - 6 \cdot 3^{x} - 55 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 6 u - 55 = 0

Solve

u^{2} - 6 u - 55 = 0 : u = 11, u = - 5

u = 11, u = - 5

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 11 : x = \frac{ln ( 11 )}{ln ( 3 )}

Solve

3^{x} = - 5 :

No Solution for

x \in R

x = \frac{ln ( 11 )}{ln ( 3 )}

4^{x} + 1 + 4^{x} - 1 = 34

5^{x - 1} = \frac{1}{625}

1.56 = 1. 5^{x}

4^{3 x} = 4^{2 (x + 7)}

2^{2 x + 2} = 128

What is the answer to 9^x-6*3^x-55=0 ?
The answer to 9^x-6*3^x-55=0 is x=(ln(11))/(ln(3))
Solve for x: 9^x-6*3^x-55=0
The solution is x=(ln(11))/(ln(3))