**
Let a, b, and x be positive real numbers such that neither a nor b equals 1
(remember x must be greater than 0). Then can be converted to
the base b by the formula .**

**Problem 4:** Convert to the base 2

**Answer:** or

**Solution:** Convert to the base 2.

The numerator can be calculated by converting the numerator to the base 10
or the base e. . The answer
can also be written
.

Note that for this problem to be valid, the base (a + b) must be greater
than zero.

**If you would like to review the rules of logarithms, click on Rules.**

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