**Let a be a positive number such that a does not equal 1, let
n be a real number, and let u and v be positive real numbers.**

**Logarithmic Rule 1:**

**Problem 5:** Simplify .

**Solution:** if you want the answer in terms of the base 3.

if you want the answer in terms of the base 10.

if you want the answer in terms of the base e.

if you want the answer in terms of the base 5.

**Note:** None of the above is valid unless *a* > 0, *b*> 0, *c* > 0, and *d* > 0.

**Check:** Suppose that a = 2, b = 3, c = 4, and d = 5. Then

and

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