The two equations y = bx and logb y = x are equivalent. They mean the same thing.
The first equation is called the exponential form and the second is called the logarithmic form. Many logarithm problems can be made much simpler by converting them to exponential form. If you can convert back and forth between these two forms, you will find exponential and logarithm problems easier to solve.
Example 1: Solve: log2 (x2) = 6.
Solution: Rewrite the problem in exponential form:
26 = x2 → 64 = x2 → x = ±8.
Example 2: Solve: ex = 35.
Solution: Rewrite the problem in logarithmic form:
ln 35 = x → x ≈ 3.56.