What is the answer to 3^{2x}-5(3^x)=-6 ?

The answer to 3^{2x}-5(3^x)=-6 is x=1,x=(ln(2))/(ln(3))

Solve for x: 3^{2x}-5(3^x)=-6

The solution is x=1,x=(ln(2))/(ln(3))

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3^{2 x} - 5 (3^{x}) = - 6

x = 1, x = \frac{ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = 1, x = 0.63092 \dots

Solution steps

3^{2 x} - 5 (3^{x}) = - 6

Apply exponent rules

(3^{x})^{2} - 5 \cdot 3^{x} = - 6

Rewrite the equation with

3^{x} = u

(u)^{2} - 5 u = - 6

Solve

u^{2} - 5 u = - 6 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

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

x = 1, x = \frac{ln ( 2 )}{ln ( 3 )}

2^{x} = \frac{1}{3}

7 e^{13 x} = 20

8^{3 x} = \frac{1}{256}

3^{x} = 9

450000 = 200000 (1.2)^{x}

What is the answer to 3^{2x}-5(3^x)=-6 ?
The answer to 3^{2x}-5(3^x)=-6 is x=1,x=(ln(2))/(ln(3))
Solve for x: 3^{2x}-5(3^x)=-6
The solution is x=1,x=(ln(2))/(ln(3))