Subjects algebra

Logarithmic Equations

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Logarithmic Equations


1. Let's start by stating what logarithmic equations are: equations that involve the logarithm of a variable. 2. A common form is $\log_a(x) = b$, which means $x = a^b$. 3. To solve logarithmic equations, we often rewrite them in exponential form to isolate the variable. 4. Example: Solve $\log_2(x) = 3$. 5. Rewrite in exponential form: $x = 2^3$. 6. Calculate $2^3 = 8$. 7. So, the solution is $x=8$. 8. Another example: Solve $\log(x+1) = 2$ where the base is 10 (common log). 9. Rewrite: $x+1 = 10^2$. 10. Calculate $10^2 = 100$. 11. Solve for $x$: $x = 100 - 1 = 99$. 12. Remember to check the domain: arguments of logarithms must be positive. 13. For example, $x+1 > 0$ so $x > -1$; $x=99$ satisfies that. 14. In summary, solve by rewriting the log equation in exponential form, then solve and check domains. 15. If you have a specific logarithmic equation, feel free to share it for a detailed solution.