Final answer:
Determining the time to double or triple an investment involves logarithmic equations and the Rule of 72 for doubling. There is no simple rule for tripling, but one can use exponential growth equations. Understanding logarithm properties is vital for solving related equations.
Step-by-step explanation:
The student is asking about determining the time it takes for an investment to double and triple using logarithmic equations and growth rates. When considering a constant annual growth rate, the Rule of 72 is a simplified way to estimate the doubling time of an investment. The formula is 72 divided by the interest rate (in percentage). For tripling, the scenario is different, as there is no common rule like the Rule of 72. However, as per the equation provided, if the base is 1.05 for a 5% growth, one would take 22.5 steps, which translates to 22.5 years for the amount to triple. Finally, to solve equations involving logarithms, you should understand properties such as log(a) - log(b) = log(a/b) and apply them accordingly to simplify and solve for the variable.