Logarithmic equation

How do you write a logarithmic equation?

To change from exponential form to logarithmic form, identify the base of the exponential equation and move the base to the other side of the equal sign and add the word “log”.

How do you read logarithmic equations?

The word logarithm, abbreviated log, is introduced to satisfy this need. This equation is rewritten as y = log 2 x. This is read as “ y equals the log of x, base 2” or “ y equals the log, base 2, of x.” which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.”

What is logarithmic function example?

For example, y = log2 8 can be rewritten as 2y = 8. Since 8 = 23 , we get y = 3. As mentioned in the beginning of this lesson, y represents the exponent, and it also represents the logarithm. Therefore, a logarithm is an exponent.

What does logarithmic mean?

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.

Can you solve logarithms without a calculator?

Example 1 Without a calculator give the exact value of each of the following logarithms. To quickly evaluate logarithms the easiest thing to do is to convert the logarithm to exponential form. In the natural logarithm the base e is the same number as in the natural exponential logarithm that we saw in the last section.

Where are logarithms used?

Using Logarithmic Functions Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

What is the range of a logarithmic function?

Therefore, the domain of the logarithmic function y=logbx is the set of positive real numbers and the range is the set of real numbers. The function rises from −∞ to ∞ as x increases if b>1 and falls from ∞ to −∞ as x increases if 0

What’s the difference between logarithmic and exponential?

logarithmic function: Any function in which an independent variable appears in the form of a logarithm. The inverse of a logarithmic function is an exponential function and vice versa. logarithm: The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number.

What does logarithmic look like?

The logarithmic function, , is spoken as “the log, base a, of x.” The logarithmic function is the inverse of the exponential function, so one can also think of logarithms by using exponential form. is the same operation as thinking “a to the y power equals x.” The common logarithmic function, written y = log x, has an

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