Pregunta
Solve the following logarithmic equation. \[ \log _{9}(x+9)=\log _{9} 13 \]
Ask by Peterson Mcguire. in the United States
Jan 22,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( x = 4 \)
Solución
To solve the logarithmic equation:
\[
\log_{9}(x + 9) = \log_{9}(13)
\]
we can use the property of logarithms that states if \(\log_b A = \log_b C\), then \(A = C\), provided that \(A, C > 0\) and \(b > 0\), \(b \neq 1\).
Applying this property:
\[
x + 9 = 13
\]
Subtract 9 from both sides to solve for \(x\):
\[
x = 13 - 9
\]
\[
x = 4
\]
**Answer:** \(4\)
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Simplifique esta solución 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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