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How Do You Convert From Logarithmic Form to Exponential Form?

Write log2 8 = 3 in exponential form.

Summary

  1. 'log' stands for 'logarithm'
  2. A logarithm is the inverse of an exponential
  3. You can go back and forth between y = bx and x = logby
  4. 'b' stands for the base
  5. 'x' is the exponent
  6. For log28 = 3, the base is 2
  7. The number that the log is equal to, 3, will be the exponent
  8. The number we're taking the log of, 8, is what the exponent will be equal to

Notes

    1. 'log' stands for 'logarithm'
    2. A logarithm is the inverse of an exponential
    3. y = bx is in exponential form
    4. This definition means that you can go back and forth between y = bx and x = logby
    1. The base in logarithmic form will be the same base in exponential form
    1. The base is the 'b' in both exponential and logarithmic forms
    1. The base is the 'b' in both exponential and logarithmic forms
    2. Logarithmic form is logby = x
    3. In this case, b = 2
    1. For log28 = 3, the base is 2 and the exponent will be 3
    2. 'log' stands for 'logarithm'
    1. Exponential form is y = bx
    2. 'b' stands for the base
    3. 'x' is the exponent
    1. Remember the definition of a logarithm:
    2. If y = bx, then x = logby
    3. 'b' stands for the base
    4. 'x' is the exponent
    5. Starting with log28 = 3, we end up with 23 = 8 in exponential form
    6. 23 = 2•2•2, which does equal 8!
    7. That means we've done this problem correctly