log3 (7x)   logb(ac^3)    

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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I suppose that you want to practice the properties of logarithms on the following logarithms:

log3 (7x) and logb (a*c^3)

To calculate the 1st logarithm, we'll have to apply the product property:

log3 (x*y) = log x + log y

Comparing, we'll get:

log3 (7x) = log3 (7) + log3 (x)

We'll apply the same property for the 2nd logarithm:

logb (a*c^3) = logb (a) + logb (c^3)

We need to apply the power property, to the second term of the sum:

logb (c^3) = 3*logb (c)

We notice that the superscript goes down in front of the logarithm.

logb (a*c^3) = logb (a) + 3*logb (c)

Therefore, applying the proper properties, the requested logarithms are:

log3 (7x) = log3 (7) + log3 (x) and logb (a*c^3) = logb (a) + 3*logb (c)