Chapter 4.FR, Problem 26E

Illustrative Applications Exercises $23$ through $26$ illustrate applications of the logarithm.

Moore’s Law According to Moore’s law, the number of transistors on a computer chip doubles about every $2\text{years}$.

a. Use the common logarithm to solve the equation ${10}^k=2^{1/2}$ for $k$.

b. Use the laws of exponents to show that an exponential function with yearly growth factor $2^{1/2}$ doubles every $2\text{years}$.

c. Explain using part b why Moore’s law says that every year the number of transistors on a computer chip increases by a factor of ${10}^k$, where $k$ is the solution to the equation in part a.