What is the answer to 9^x=3^{x+3}-5 ?

The answer to 9^x=3^{x+3}-5 is x=(ln((27+sqrt(709))/2))/(ln(3)),x=(ln((27-sqrt(709))/2))/(ln(3))

Solve for x: 9^x=3^{x+3}-5

The solution is x=(ln((27+sqrt(709))/2))/(ln(3)),x=(ln((27-sqrt(709))/2))/(ln(3))

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9^{x} = 3^{x + 3} - 5

x = \frac{ln ( \frac{27 + 709}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{27 - 709}{2} )}{ln ( 3 )}

Decimal Notation

x = 2.99369 \dots, x = - 1.52871 \dots

Solution steps

9^{x} = 3^{x + 3} - 5

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} = u \cdot 3^{3} - 5 : u = \frac{27 + 709}{2}, u = \frac{27 - 709}{2}

u = \frac{27 + 709}{2}, u = \frac{27 - 709}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{27 + 709}{2} : x = \frac{ln ( \frac{27 + 709}{2} )}{ln ( 3 )}

Solve

3^{x} = \frac{27 - 709}{2} : x = \frac{ln ( \frac{27 - 709}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{27 + 709}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{27 - 709}{2} )}{ln ( 3 )}

85 = 1 1^{x}

5^{x + 1} = 7^{5 x - 1}

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

What is the answer to 9^x=3^{x+3}-5 ?
The answer to 9^x=3^{x+3}-5 is x=(ln((27+sqrt(709))/2))/(ln(3)),x=(ln((27-sqrt(709))/2))/(ln(3))
Solve for x: 9^x=3^{x+3}-5
The solution is x=(ln((27+sqrt(709))/2))/(ln(3)),x=(ln((27-sqrt(709))/2))/(ln(3))