The given function is:
$f(x) = \log_{10}(x)$

Transformations Applied

1. Vertical Stretch by 7 → Multiply $f(x)$ by 7:
   $g(x) = 7\log_{10}(x)$
2. Shift Left by 4 → Replace $x$ with $x + 4$:
   $g(x) = 7\log_{10}(x + 4)$
3. Shift Down by 5 → Subtract 5 from the function:
   $g(x) = 7\log_{10}(x + 4) - 5$

Final Answer

$g(x) = 7\log_{10}(x + 4) - 5$

Would you like a step-by-step explanation of how each transformation affects the graph?

Related Questions:

1. How does a vertical stretch affect the shape of a logarithmic graph?
2. What happens when a logarithmic function is shifted horizontally?
3. How do you determine the new domain of a transformed logarithmic function?
4. Can this function be rewritten in exponential form?
5. How does shifting down by 5 affect the range of the function?

Tip:
Always apply horizontal transformations before vertical ones to avoid confusion in function modifications.