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How Do You Convert From Natural Logarithmic Form to Exponential Form?

Write ln9=x in exponential form with base e.

Summary

  1. 'ln' stands for natural logarithm
  2. A natural logarithm is just a logarithm with a base of 'e'
  3. 'e' is the natural base and is approximately equal to 2.718
  4. y = bx is in exponential form and x = logby is in logarithmic form
  5. The definition of logarithms says that these two equations are equivalent, so we can convert back and forth between them
  6. 'b' stands for 'base' and 'x' is the exponent
  7. x = ln(y) is the same thing as x = logey

Notes

    1. Exponential form is y = bx
    2. Logarithmic form is x = logby
    3. 'b' stands for 'base' and 'x' is the exponent
    4. The definition of a logarithm tells us that these two forms are equivalent
    5. So we can convert back and forth between the two forms
    1. The definition for a natural logarithm is almost identical to the definition for a logarithm
    2. The only difference is that the base of a natural logarithm is always the number 'e'
    3. 'e' is called the 'natural base' and is approximately equal to 2.718
    1. Usually when we work with natural logs we use 'ln' instead of 'loge', but they mean the same thing
    2. Here if we use 'loge' instead, it will be easier to identify what we need to know to rewrite this in exponential form
    1. The base of the exponent is the same as the base of the logarithm
    1. The base is the small number just to the right and below the 'log'
    2. Since we rewrote our natural log as loge9 = x, we can see that our base is 'e'
    1. Our logarithm is loge9 = x
    1. Our logarithm is loge9 = x
    2. 9 is the number we're taking the log of, so y = 9
    3. 'y' is what the exponential function will be equal to when we convert to exponential form
    1. Taking a logarithm is basically like trying to find an unknown exponent
    2. When we rewrite this equation in exponential form, the number we don't know, 'x', will be in the exponent
    1. Since we started with a natural logarithm, the base of our exponent is 'e'
    2. 'e' is the natural base and is approximately 2.71828
    3. The exponent is the number our logarithmic expression was equal to
    4. The exponential expression equals the number we were taking the log of, 9