What is the answer to 9^x+20=3^{x+2} ?

The answer to 9^x+20=3^{x+2} is x=(ln(5))/(ln(3)),x=(2ln(2))/(ln(3))

Solve for x: 9^x+20=3^{x+2}

The solution is x=(ln(5))/(ln(3)),x=(2ln(2))/(ln(3))

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9^{x} + 20 = 3^{x + 2}

x = \frac{ln ( 5 )}{ln ( 3 )}, x = \frac{2 ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = 1.46497 \dots, x = 1.26185 \dots

Solution steps

9^{x} + 20 = 3^{x + 2}

Apply exponent rules

(3^{x})^{2} + 20 = 3^{x} \cdot 3^{2}

Rewrite the equation with

3^{x} = u

(u)^{2} + 20 = u \cdot 3^{2}

Solve

u^{2} + 20 = u \cdot 3^{2} : u = 5, u = 4

u = 5, u = 4

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 5 : x = \frac{ln ( 5 )}{ln ( 3 )}

Solve

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

x = \frac{ln ( 5 )}{ln ( 3 )}, x = \frac{2 ln ( 2 )}{ln ( 3 )}

9 (3^{2 x}) - 28 (3^{x}) + 3 = 0

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

8 + 0.04 x = 6 (1.02)^{x}

x^{10} = e^{x}

4^{x} = \frac{8}{1 6 ^{x}}

What is the answer to 9^x+20=3^{x+2} ?
The answer to 9^x+20=3^{x+2} is x=(ln(5))/(ln(3)),x=(2ln(2))/(ln(3))
Solve for x: 9^x+20=3^{x+2}
The solution is x=(ln(5))/(ln(3)),x=(2ln(2))/(ln(3))