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How are logarithms calculated?

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. For example, 23 = 8. Therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

What is the formula for logarithmic functions?

The logarithmic function y = Logan is defined to be equivalent to the exponential equation x = a. y = Logan only under the following conditions: x = a, a > 0, and a1. It is called the logarithmic function with base a. Consider what the inverse of the exponential function means: x = a.

How do you find the logarithmic function?

The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logo x is read, y equals log to the base b of x, or more simply, y equals log base b of x. As with exponential functions, b > 0 and b 1.

What is logarithmic function example?

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. For example, 23 = 8. Therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

What is a logarithmic equation?

Logarithmic Equations. Logarithmic equations contain logarithmic expressions and constants. A logarithm is another way to write an exponent and is defined by if and only if. If one side of a logarithmic equation contains more than one logarithm, use the properties of logarithms to condense it into a single logarithm.

How is the logarithmic function defined?

Definition of logarithmic function. a function (such as y = logo x or y = LN x) that is the inverse of an exponential function (such as y = ax or y = ex) so that the independent variable appears in a logarithm.

How do you solve equations using logarithms?

Keep the exponential expression by itself on one side of the equation. Get the logarithms of both sides of the equation. You can use any bases for logs. Solve for the variable. Keep the answer exact or give decimal approximations.

How do you get rid of a log?

Start with the equation: For example, log x = log (x — 2) + 3. Rearrange the terms: log x — log (x — 2) = 3. Apply the law of logarithms: log (x/x-2) = 3. Raise both sides to a power of 10: x ÷ (x — 2) = 3. Solve for x: x = 3.

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