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

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

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

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

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

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

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

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

u = 2, u = - \frac{1}{3}

Substitute back

u = 3^{x},

solve for

x

Solve

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

Solve

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

No Solution for

x \in R

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

1 = e^{c}

e^{\frac{2}{3} t} = e^{10}

2 5^{9 x - 8} = 120

4^{x + 3} = 1 6^{x - 5}

3 + 2^{x} + 1 = [24 - (2^{2} - 1)]

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