What is the answer to 3^{5x+2}+9^{2x}=81 ?

The answer to 3^{5x+2}+9^{2x}=81 is x=0.38723…

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3^{5x+2}+9^{2x}=81

3^{5 x + 2} + 9^{2 x} = 81

x = 0.38723 \dots

Solution steps

3^{5 x + 2} + 9^{2 x} = 81

Apply exponent rules

(3^{x})^{5} \cdot 3^{2} + (3^{x})^{4} = 81

Rewrite the equation with

3^{x} = u

(u)^{5} \cdot 3^{2} + (u)^{4} = 81

Solve

u^{5} \cdot 3^{2} + u^{4} = 81 : u \approx 1.53024 \dots

u \approx 1.53024 \dots

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1.53024 \dots : x = 0.38723 \dots

x = 0.38723 \dots

3^{x + 2} = 0

9^{y} = 27

9 = 2^{x}

e^{(0.1) k} = 5

2 e^{3 x} - 1 = 5

What is the answer to 3^{5x+2}+9^{2x}=81 ?
The answer to 3^{5x+2}+9^{2x}=81 is x=0.38723…
Solve for x: 3^{5x+2}+9^{2x}=81
The solution is x=0.38723…