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Solve the following logarithmic equation. \[ \log _{9}(x+9)=\log _{9} 13 \]

Ask by Peterson Mcguire. in the United States
Jan 22,2025

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\( x = 4 \)

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The Deep Dive

To solve the logarithmic equation \[ \log _{9}(x+9)=\log _{9} 13, \] we can use the property that if \(\log_b(a) = \log_b(c)\), then \(a = c\). Applying this principle gives us: \[ x + 9 = 13. \] Now, we can solve for \(x\): \[ x = 13 - 9, \] \[ x = 4. \] Thus, the solution to the equation is \[ \boxed{4}. \]

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