What is the answer to 9^{(x+1)}+1=10(3^x) ?

The answer to 9^{(x+1)}+1=10(3^x) is x=0,x=-2

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9^{(x+1)}+1=10(3^x)

9^{(x + 1)} + 1 = 10 (3^{x})

x = 0, x = - 2

Solution steps

9^{(x + 1)} + 1 = 10 (3^{x})

Apply exponent rules

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

Rewrite the equation with

3^{x} = u

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

Solve

u^{2} \cdot 3^{2} + 1 = 10 u : u = 1, u = \frac{1}{9}

u = 1, u = \frac{1}{9}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 1 : x = 0

Solve

3^{x} = \frac{1}{9} : x = - 2

x = 0, x = - 2

3^{y} = 27

5^{x} = 5^{9}

\frac{1}{25} = 5^{n}

e^{- x} (1 + x) = 0.005

e^{3 x} = 2 + b

What is the answer to 9^{(x+1)}+1=10(3^x) ?
The answer to 9^{(x+1)}+1=10(3^x) is x=0,x=-2
Solve for x: 9^{(x+1)}+1=10(3^x)
The solution is x=0,x=-2