Use complete sentences to describe how logarithms can aid in difficult calculations.

in mathematics, the logarithm is the inverse function to exponentiation. that means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. in the simplest case the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. the logarithm of x to base b is denoted as logb (x) (or, without parentheses, as logb x, or even without explicit base as log x, when no confusion is possible).

more generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm for any two positive real numbers b and x where b is not equal to 1, is always a unique real number y.

more explicitly, the defining relation between exponentiation and logarithm is:

for example, log2 64 = 6, as 64 = 26.

the logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. the natural logarithm has the number e (that is b ≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. the binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

step-by-step explanation:

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