Final answer:
To convert log base b of x equals y to exponential form, you write it as b to the power of y equals x. This shows that exponentiation and logarithms are inverse operations and is essential for solving equations involving exponential growth.
Step-by-step explanation:
To convert 'log base b of x equals y' to exponential form, you use the fundamental property that logarithms and exponentiation are inverse operations.
The statement 'log base b of x equals y' means that b raised to the power of y equals x. Mathematically, this is written as by = x.
Let's use an example: If we have log base 3 of 27 equals 3, this means that 3 raised to the power of 3 equals 27, so in exponential form, it's 33 = 27.
Understanding this conversion is a key part of working with exponents and logarithms, including common logarithms and natural logarithms. The ability to switch between these forms is critical in algebra, and helps with solving equatíons, especially when dealing with exponential growth and decay problems.