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Ĭlick HERE to see a detailed solution to problem 11.Ĭlick HERE to see a detailed solution to problem 12.Ĭlick HERE to return to the original list of various types of calculus problems. Determine the slope of the line perpendicular to the graph of f at x=1. Ĭlick HERE to see a detailed solution to problem 10. Find an equation of the line tangent to the graph of f at x=1. Therefore, the value of log e to the base 10 as follows. According to the definition of the logarithmic function, it is observed that. The following problems range in difficulty from average to challenging.Ĭlick HERE to see a detailed solution to problem 1.Ĭlick HERE to see a detailed solution to problem 2.Ĭlick HERE to see a detailed solution to problem 3.Ĭlick HERE to see a detailed solution to problem 4.Ĭlick HERE to see a detailed solution to problem 5.Ĭlick HERE to see a detailed solution to problem 6.Ĭlick HERE to see a detailed solution to problem 7.Ĭlick HERE to see a detailed solution to problem 8.Ĭlick HERE to see a detailed solution to problem 9. The log function of e to the base 10 is denoted as log 10 e. Logarithmic function is the inverse Mathematical function of exponential function.
For example, logarithm to the base 10 of 1000 is 3 because 10 raised to the power 3 is 1000. Though the following properties and methods are true for a logarithm of any base, only the natural logarithm (base e, where eĪVOID THE FOLLOWING LIST OF COMMON MISTAKES Value of Log e: The power to which a number should be raised to get the specified number is called the logarithm of that number. It requires deft algebra skills and careful use of the following unpopular, but well-known, properties of logarithms. Logarithmic differentiation will provide a way to differentiate a function of this type. An example and two COMMON INCORRECT SOLUTIONS are :īOTH OF THESE SOLUTIONS ARE WRONG because the ordinary rules of differentiation do not apply. For example, in the problems that follow, you will be asked to differentiate expressions where a variable is raised to a variable power. It is a means of differentiating algebraically complicated functions or functions for which the ordinary rules of differentiation do not apply.
Since we know how to differentiate exponentials, we can use implicit differentiation to find the derivatives of ln(x) and loga(x). The following problems illustrate the process of logarithmic differentiation. We define log functions as the inverses of exponentials: y ln(x) xe y.