Question

1. solve: $\log_{3} 4 + \log_{3}(x - 5) = 3$

Explanation:

Step1: Combine logs via product rule

$\log_3[4(x-5)] = 3$

Step2: Convert to exponential form

$4(x-5) = 3^3$

Step3: Simplify right-hand side

$4(x-5) = 27$

Step4: Isolate $(x-5)$

$x-5 = \frac{27}{4}$

Step5: Solve for $x$

$x = \frac{27}{4} + 5 = \frac{27}{4} + \frac{20}{4}$

Answer:

$\frac{47}{4}$