Quiz: Mastering Logarithms – Practice Questions (Set 1)

This quiz focuses on the key concepts of logarithmic functions, as explained in the video on this page. It tests your understanding of logarithms, mathematical expressions, and equations involving logarithms, square roots, and other operations. Please complete the quiz without relying on external resources. If your answers are incorrect, you can retake the quiz and aim to get them all correct. If you notice any errors in the questions or answers, please leave a comment. Enjoy the quiz!

1. 
Simplify: $log_5(25) + log_5(1/5)$

2. 
Simplify: $log_3(81) − log_3(9) + log_3(27)$

3. 
If $log_b(2) = 0.3$ and $log_b(3) = 0.5$, evaluate $log_b(18)$

4. 
Simplify: $log_7(49) + 2log_7(3) − log_7(21)$

5. 
Solve the equation: $log_2(\sqrt{x + 4}) = 3$

6. 
Solve for $x$: $log_2(x + 1) + log_2(x - 1) = 3$

7. 
Solve for $x$: $log_2(x) + log_2(x - 2) = 3$

8. 
Solve for $x$: $log_3(x + 1) - log_3(x - 1) = 1$

9. 
Solve for $x$: $log_3(x^2 - 7) > 2$

10. 
If $log_{10}(2) = 0.3010$ and $log_{10}(3) = 0.4771$, then evaluate $log_{10}(12)$

11. 
Simplify: $\frac{log_2(32)}{log_2(8)} + log_4(16)$

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