To find the value of the function f(x) = log₃(5x) minus g(x) = log₃(x), we first need to understand the properties of logarithms.
Using the properties of logarithms, we can rewrite the function f(x):
- f(x) = log₃(5x)
This can be broken down using the property of logarithms that states logb(mn) = logb(m) + logb(n). Applying this property, we have:
- f(x) = log₃(5) + log₃(x)
Now, we can substitute this back into our original expression to find f(x) – g(x):
- f(x) – g(x) = (log₃(5) + log₃(x)) – log₃(x)
- f(x) – g(x) = log₃(5)
In conclusion, when we calculate f(x) – g(x), the x terms cancel out, leaving us with:
Final Result:
f(x) – g(x) = log₃(5)