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you should include the definition of logarithms how to solve logarithmic equations how they are used in applications of math and everyday life how to graph logarithms explain how logarithms are the inverses of exponential how to graph exponentials importance of exponential functions(growth and decay ex.) pandemics, population)
Logarithmic functions are converted to become exponential functions because both are inverses of one another.
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
Equalities transformed using equal quantities are equal for most common bainary opeartions - with a few exceptions.The operations include addition, subtraction, mutiplication as well as division (when defined).Exponentiation to integer powers is included but not fractional powers. If defined, logarithms to the same base are equal. The basic trigonometric functions are also valid transformations but their inverses (the arc functions) are not.Equalities transformed using equal quantities are equal for most common bainary opeartions - with a few exceptions.The operations include addition, subtraction, mutiplication as well as division (when defined).Exponentiation to integer powers is included but not fractional powers. If defined, logarithms to the same base are equal. The basic trigonometric functions are also valid transformations but their inverses (the arc functions) are not.Equalities transformed using equal quantities are equal for most common bainary opeartions - with a few exceptions.The operations include addition, subtraction, mutiplication as well as division (when defined).Exponentiation to integer powers is included but not fractional powers. If defined, logarithms to the same base are equal. The basic trigonometric functions are also valid transformations but their inverses (the arc functions) are not.Equalities transformed using equal quantities are equal for most common bainary opeartions - with a few exceptions.The operations include addition, subtraction, mutiplication as well as division (when defined).Exponentiation to integer powers is included but not fractional powers. If defined, logarithms to the same base are equal. The basic trigonometric functions are also valid transformations but their inverses (the arc functions) are not.
The Web site integrals.wolfram.com gives the following:integral of sin2x/x = (1/2) (log x - Ci(2 x))Ci is the cosine integral, a special function. Look at the site for a more detailed description.What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.The Web site integrals.wolfram.com gives the following:integral of sin2x/x = (1/2) (log x - Ci(2 x))Ci is the cosine integral, a special function. Look at the site for a more detailed description.What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.The Web site integrals.wolfram.com gives the following:integral of sin2x/x = (1/2) (log x - Ci(2 x))Ci is the cosine integral, a special function. Look at the site for a more detailed description.What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.The Web site integrals.wolfram.com gives the following:integral of sin2x/x = (1/2) (log x - Ci(2 x))Ci is the cosine integral, a special function. Look at the site for a more detailed description.What this really means is that this integral can NOT be solved with the so-called elementary functions, i.e., using only polynomials, roots, trigonometric functions, natural logarithms, and the inverses of some of these.