What is the answer to 3^{2x+1}-(16)3^x+5=0 ?

The answer to 3^{2x+1}-(16)3^x+5=0 is x=(ln(5))/(ln(3)),x=-1

Solve for x: 3^{2x+1}-(16)3^x+5=0

The solution is x=(ln(5))/(ln(3)),x=-1

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3^{2 x + 1} - (16) 3^{x} + 5 = 0

x = \frac{ln ( 5 )}{ln ( 3 )}, x = - 1

Decimal Notation

x = 1.46497 \dots, x = - 1

Solution steps

3^{2 x + 1} - (16) \cdot 3^{x} + 5 = 0

Apply exponent rules

(3^{x})^{2} \cdot 3^{1} - 16 \cdot 3^{x} + 5 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} \cdot 3^{1} - 16 u + 5 = 0

Solve

u^{2} \cdot 3^{1} - 16 u + 5 = 0 : u = 5, u = \frac{1}{3}

u = 5, u = \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 5 : x = \frac{ln ( 5 )}{ln ( 3 )}

Solve

3^{x} = \frac{1}{3} : x = - 1

x = \frac{ln ( 5 )}{ln ( 3 )}, x = - 1

4 = 240 1^{x} - 3

4^{3 x - 3} = 1 6^{2 x - 1}

1500000000 = 766 e^{0.0182 t}

9^{x} + 3 = 4 (3^{x})

0 = 3 - 2^{x}

What is the answer to 3^{2x+1}-(16)3^x+5=0 ?
The answer to 3^{2x+1}-(16)3^x+5=0 is x=(ln(5))/(ln(3)),x=-1
Solve for x: 3^{2x+1}-(16)3^x+5=0
The solution is x=(ln(5))/(ln(3)),x=-1