What is the answer to 9^x-4=3^{x+1} ?

The answer to 9^x-4=3^{x+1} is x=(2ln(2))/(ln(3))

Solve for x: 9^x-4=3^{x+1}

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

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9^{x} - 4 = 3^{x + 1}

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

Decimal Notation

x = 1.26185 \dots

Solution steps

9^{x} - 4 = 3^{x + 1}

Apply exponent rules

(3^{x})^{2} - 4 = 3^{x} \cdot 3^{1}

Rewrite the equation with

3^{x} = u

(u)^{2} - 4 = u \cdot 3^{1}

Solve

u^{2} - 4 = u \cdot 3^{1} : u = 4, u = - 1

u = 4, u = - 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 3 )}

Solve

3^{x} = - 1 :

No Solution for

x \in R

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

e^{x} + 6 \cdot e^{- x} = 5

100 - 98 y + 980 (1 - e^{- 0.1 y}) = 0

4 e^{2 x} = 0

9 \cdot 2^{x - 1} = 2 \cdot 3^{x}

2^{(x^{2} - 10 x + 25)} - 5 = 11

What is the answer to 9^x-4=3^{x+1} ?
The answer to 9^x-4=3^{x+1} is x=(2ln(2))/(ln(3))
Solve for x: 9^x-4=3^{x+1}
The solution is x=(2ln(2))/(ln(3))