In equivalent logarithmic form?

Last Update: April 20, 2022

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Asked by: Miss Summer Tremblay
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Every equation that is in exponential form has an equivalent logarithmic form, and vice versa. Both equations have a 'b,' the base, an x, and a y. These two equations are equivalent, just like these two equations are equivalent: y = x + 9 and y - 9 = x. Using algebra, you can get from one to the other.

How do you find equivalent logarithms?

On the right-hand side above, "logb(y) = x" is the equivalent logarithmic statement, which is pronounced "log-base-b of y equals x"; The value of the subscripted "b" is "the base of the logarithm", just as b is the base in the exponential expression "bx".

How do you convert to logarithmic form?

To convert from exponential to logarithmic form, we follow the same steps in reverse. We identify the base b, exponent x, and output y. Then we write x=logb(y) x = l o g b ( y ) .

What is equivalent exponential form?

Exponential form is y = bx. Logarithmic form is x = logby. 'b' stands for 'base' and 'x' is the exponent. The definition of a logarithm tells us that these two forms are equivalent. So we can convert back and forth between the two forms.

What is an example of exponential form?

Exponential notation is an alternative method of expressing numbers. Exponential numbers take the form an, where a is multiplied by itself n times. A simple example is 8=23=2×2×2. ... For example, 5 ×103 is the scientific notation for the number 5000, while 3.25×102is the scientific notation for the number 325.

How to convert between logarithmic form and exponential

22 related questions found

What is exponential form for logs?

So, a log is an exponent ! ... y=logbx if and only if by=x for all x>0 and 0<b≠1 . Example 1: Write log5125=3 in exponential form.

How do you know if a graph is a logarithmic function?

The logarithmic function graph passes through the point (1, 0), which is the inverse of (0, 1) for an exponential function. The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1.

What is the base of a natural log?

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

Is logarithmic the same as exponential?

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. ... So you see a logarithm is nothing more than an exponent.

Where do you use logarithms in real life?

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).

Can the base of a log be negative?

While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers.

What is the general form of a logarithmic function?

The "basic" logarithmic function is the function, y=logbx, where x, b>0 and b≠1.

How do you solve logarithmic equations with different bases?

To solve this type of problem:
  1. Step 1: Change the Base to 10. Using the change of base formula, you have. ...
  2. Step 2: Solve for the Numerator and Denominator. Since your calculator is equipped to solve base-10 logarithms explicitly, you can quickly find that log 50 = 1.699 and log 2 = 0.3010.
  3. Step 3: Divide to Get the Solution.

What is logarithmic function example?

For example, 32 = 2 × 2 × 2 × 2 × 2 = 22. The exponential function 22 is read as “two raised by the exponent of five” or “two raised to power five” or “two raised to the fifth power.” Then the logarithmic function is given by; f(x) = log b x = y, where b is the base, y is the exponent, and x is the argument.

How do you tell if a graph is exponential or logarithmic?

The inverse of an exponential function is a logarithmic function. Remember that the inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.

What point is on every logarithmic function?

This is because the range of every exponential function is (0, inf), and logarithmic functions are inverses of exponential functions. Since the graphs of all exponential functions contain the point (0,1), the graphs of all logarithmic functions contain the point (1,0), the reflection of (0,1) in the line y = x.