What is the answer to 9^x-16*3^x+27=0 ?

The answer to 9^x-16*3^x+27=0 is x=(ln(8+sqrt(37)))/(ln(3)),x=(ln(8-sqrt(37)))/(ln(3))

Solve for x: 9^x-16*3^x+27=0

The solution is x=(ln(8+sqrt(37)))/(ln(3)),x=(ln(8-sqrt(37)))/(ln(3))

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9^{x} - 16 \cdot 3^{x} + 27 = 0

x = \frac{ln ( 8 + 37 )}{ln ( 3 )}, x = \frac{ln ( 8 - 37 )}{ln ( 3 )}

Decimal Notation

x = 2.40753 \dots, x = 0.59246 \dots

Solution steps

9^{x} - 16 \cdot 3^{x} + 27 = 0

Apply exponent rules

(3^{x})^{2} - 16 \cdot 3^{x} + 27 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 16 u + 27 = 0

Solve

u^{2} - 16 u + 27 = 0 : u = 8 + 37, u = 8 - 37

u = 8 + 37, u = 8 - 37

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 8 + 37 : x = \frac{ln ( 8 + 37 )}{ln ( 3 )}

Solve

3^{x} = 8 - 37 : x = \frac{ln ( 8 - 37 )}{ln ( 3 )}

x = \frac{ln ( 8 + 37 )}{ln ( 3 )}, x = \frac{ln ( 8 - 37 )}{ln ( 3 )}

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

2 5^{2 x + 1} - 1 = 143

11 (1 + e^{- x})^{- 1} = 3

1536 = 6 (2)^{n - 1}

5^{2 x + 4} - 2 5^{x - 1} = 78120

What is the answer to 9^x-16*3^x+27=0 ?
The answer to 9^x-16*3^x+27=0 is x=(ln(8+sqrt(37)))/(ln(3)),x=(ln(8-sqrt(37)))/(ln(3))
Solve for x: 9^x-16*3^x+27=0
The solution is x=(ln(8+sqrt(37)))/(ln(3)),x=(ln(8-sqrt(37)))/(ln(3))