What is the answer to 9^x+9=10*3^x ?

The answer to 9^x+9=10*3^x is x=2,x=0

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9^x+9=10*3^x

9^{x} + 9 = 10 \cdot 3^{x}

x = 2, x = 0

Solution steps

9^{x} + 9 = 10 \cdot 3^{x}

Apply exponent rules

(3^{x})^{2} + 9 = 10 \cdot 3^{x}

Rewrite the equation with

3^{x} = u

(u)^{2} + 9 = 10 u

Solve

u^{2} + 9 = 10 u : u = 9, u = 1

u = 9, u = 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = 1 : x = 0

x = 2, x = 0

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