What is the answer to 81=10*3^{x+1}-9^x ?

The answer to 81=10*3^{x+1}-9^x is x=1,x=3

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81=10*3^{x+1}-9^x

81 = 10 \cdot 3^{x + 1} - 9^{x}

x = 1, x = 3

Solution steps

81 = 10 \cdot 3^{x + 1} - 9^{x}

Apply exponent rules

81 = 10 \cdot 3^{x} \cdot 3^{1} - (3^{x})^{2}

Rewrite the equation with

3^{x} = u

81 = 10 u \cdot 3^{1} - (u)^{2}

Solve

81 = 10 u \cdot 3^{1} - u^{2} : u = 3, u = 27

u = 3, u = 27

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

3^{x} = 27 : x = 3

x = 1, x = 3

2^{x - 1} + 2^{x + 1} = 320

3^{2 x} + 5 \cdot 3^{x} = 864

1.25 = 1.3 3^{x}

e^{x} = 5.7

2^{2} x - 6. 2^{x} + 8 = 0

What is the answer to 81=10*3^{x+1}-9^x ?
The answer to 81=10*3^{x+1}-9^x is x=1,x=3
Solve for x: 81=10*3^{x+1}-9^x
The solution is x=1,x=3