Questions: Solve the equation 3^(x+1)=9. If no solution exists, enter None. x=

Solve the equation 3^(x+1)=9. If no solution exists, enter None. x=
Transcript text: Solve the equation $3^{x+1}=9$. If no solution exists, enter None. $x=$
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Solution

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Solution Steps

Step 1: Rewrite the equation using the same base

The equation is \(3^{x+1} = 9\). Notice that \(9\) can be written as a power of \(3\): \[ 9 = 3^2. \] Thus, the equation becomes: \[ 3^{x+1} = 3^2. \]

Step 2: Equate the exponents

Since the bases are the same, the exponents must be equal: \[ x + 1 = 2. \]

Step 3: Solve for \(x\)

Subtract \(1\) from both sides to solve for \(x\): \[ x = 2 - 1, \] \[ x = 1. \]

Final Answer

\[ \boxed{x = 1} \]

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