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How Do You Simplify Logarithms Using the Product Property?

Simplify log59 + log54.

Summary

  1. This property lets you add together logarithms with the same base
  2. 'b' is the base of the logarithm: the little number to the left of the 'log'
  3. 'm' and 'n' are the values we're taking the logarithm of
  4. In order to use this property, the logarithms must have the SAME BASE
  5. The base, 'b', is 5 for both logarithms, so we CAN use the Product Property
  6. We can plug 9 in for 'm' and 4 in for 'n' into the formula

Notes

    1. This property lets you add together logarithms with the same base
    1. This property lets you add together logarithms with the same base
    2. 'm' and 'n' are the values we're taking the logarithm of
    3. 'b' is the base of the logarithm: the little number to the left of the 'log'
    4. This property can only be used if the logarithms have the SAME BASE
    1. In order to use this property, the logarithms must have the same base
    1. b = 5 for both logarithms
    2. That means we CAN use the Product Property of Logarithms here!
    1. Rewrite the problem as one logarithm
    2. b = 5
    3. m = 9
    4. n = 4
    5. Plugging the values into the formula gives us log5(9•4)
    1. Now we just need to multiply what's inside the parentheses!
    1. 9•4 = 36