Question

Solve for \( x \): \( \log(x) + \log(5) = \log(20) \).

Hint:

When logs with the same base are equal, you can equate their arguments directly after combining terms using log rules.

Answer 1

Concept: Use logarithmic properties. One key identity is: \[ \log a + \log b = \log (ab) \] This allows combining logarithmic expressions into a single logarithm. 
Step 1: Apply Log Addition Rule Given: \[ \log(x) + \log(5) = \log(20) \] Using: \[ \log a + \log b = \log(ab) \] \[ \log(5x) = \log(20) \] Step 2: Remove Logarithm If: \[ \log A = \log B \] Then: \[ A = B \] So, \[ 5x = 20 \] Step 3: Solve for \( x \) \[ x = \frac{20}{5} = 4 \] \[ \boxed{x = 4} \]