Today, we study applicatons of logarithmic.
Suppose you invest 1000$ at 8% compounded continuously and wish to know how much time must pass for your investment to double in value to 2000$. According to the formula derived in before section, the value of your account after t years will be 1000e0.08t ,so to find the doubling time for your account, you must solve for t in the equation
1000e0.08t =2000
or, by dividing both sides by 1000
We will answer the question about doubling time in Example. Solving an exponential equation such as this involves using logarithms, which reverse the process of exponentiation. Logarithms play an important role in a variety of application, such as measuring the capacity of transmission channel and in the famous Richter scale for measuring eathquake intensity. In this section, we examine the basic properties of logarithmic functions and a few application.
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