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bballwaterboy
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Just curious, since we're discussing them this week in my class. Why do we need logarithms? Aren't they just a concoction to express exponents?
Try differentiating ##f(x) = x^x##bballwaterboy said:Just curious, since we're discussing them this week in my class. Why do we need logarithms? Aren't they just a concoction to express exponents?
PeroK said:Try differentiating ##f(x) = x^x##
Yeah, me, too. I still own about five of them.Doug Huffman said:LOL Why do we need calculators? Aren't they just a crutch to do calculations?
Calculators and computers were prohibited in my schooling and early in my professional career. I can still use a slide rule.
PeroK said:Try differentiating ##f(x) = x^x##
Well, then you have probably covered exponential functions such as y = ex, y = 10x, and the like. Log functions, in an appropriate base, are the inverses of the exponential functions. For example,bballwaterboy said:Don't know what you mean. Haven't covered that yet.
bolbteppa said:You can just view the logarithm as a way to turn multiplicative things into additive things
Or, "Same reason we have subtraction and division when we already have addition and multiplication."?homeomorphic said:Once you decide that exponents are needed and inverse functions are needed, you pretty much already have logarithms. Calling them log is just giving a name to something that is already there, namely, the inverse of an exponential function.
No, logarithms are still widely used in various fields of science, including mathematics, physics, chemistry, and biology. They are essential tools for solving complex equations and representing data in a more manageable form.
Logarithms and exponents are inverse operations of each other. While exponents represent repeated multiplication, logarithms represent the power to which a base number must be raised to get a given value. For example, in the equation 2^3 = 8, 3 is the exponent, and log base 2 of 8 is 3.
While exponents are useful for representing numbers with large values, logarithms are better for representing very small or very large values. They also help in simplifying complex equations and making data easier to interpret.
Logarithms are commonly used in situations involving exponential growth or decay, such as in population growth, radioactive decay, and compound interest calculations. They are also used in data analysis, signal processing, and other mathematical applications.
No, you do not need to memorize logarithm formulas. As long as you understand the basic concept of logarithms and how to use a calculator or computer to calculate them, you can easily solve logarithmic equations and problems.