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

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

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

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

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

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

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} = u \cdot 3^{1} + 4 : 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 )}

ln (e^{8 x}) = 96

t, 40 = 12 0^{0.4 t} + 25

(\frac{1}{5})^{x - 2} = 2 5^{x - 2}

5^{x + 1} + 5^{x} + 5^{x - 2} - 151 = 0

2^{2 x} - 2^{x} - 12 = 0

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