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How Do You Convert From Exponential Form to Logarithmic Form?

Write 23 = 8 in logarithmic form.

Summary

  1. 23 = 8 is in exponential form
  2. Exponential form is y = bx
  3. Logarithmic form is x = logby
  4. The definition of a logarithm tells us that these two forms are equivalent
  5. So you can go back and forth between y = bx and x = logby
  6. 'log' stands for 'logarithm'
  7. 'b' stands for the base
  8. 'x' is the exponent in exponential form
  9. In logarithmic form, 'x' is the number the log is equal to

Notes

    1. Exponential form is y = bx
    2. Logarithmic form is x = logby
    3. The definition of a logarithm tells us that these two forms are equivalent
    4. So you can go back and forth between y = bx and x = logby
    5. 23 = 8 is in exponential form
    6. 'b' stands for the base
    7. 'x' is the exponent in exponential form
    8. In logarithmic form, 'x' is the number the log is equal to
    1. Exponential form is y = bx
    2. Here we want to identify 'b', the base
    1. 23 = 8 is in exponential form
    2. If we can find the base in exponential form, we'll have the base for the logarithm
    3. 'b' stands for the base
    1. 23 = 8 is in exponential form
    2. Exponential form is y = bx, where 'b' stands for the base
    3. So our 'b' here is 2
    1. If we find the exponent in exponential form, we'll have the value the logarithm is equal to
    2. 23 = 8 is in exponential form
    3. Exponential form is y = bx, where 'x' is the exponent
    4. So our 'x' is 3
    1. Logarithmic form is x = logby
    1. Now we can take the numbers we got from our function in exponential form and rearrange them into logarithmic form
    2. Remember, we had 23 = 8 in exponential form
    3. If we plug the numbers we identified in Steps 2 and 3 into logarithmic form, we get log28 = 3