Mastering The Properties Of Ln: Simplify And Solve Logarithmic Equations

Some common properties of ln are: ln(xy) =.__________ ,ln(x/y) =.__________and ln(xr) =__________

lnx+ lny; lnx−lny;rlnx

Some common properties of ln are:

1. ln(xy) = ln(x) + ln(y)
This property states that the natural logarithm of the product of two numbers is equal to the sum of the natural logarithms of the individual numbers. For example, ln(2*3) = ln(2) + ln(3) = 0.693 + 1.099 =1.792.

2. ln(x/y) = ln(x) – ln(y)
This property states that the natural logarithm of the quotient of two numbers is equal to the difference of the natural logarithms of the individual numbers. For example, ln(6/2) = ln(6) – ln(2) = 1.792 – 0.693 = 1.099.

3. ln(x^r) = r*ln(x)
This property states that the natural logarithm of a number raised to a power is equal to the product of the power and the natural logarithm of the base number. For example, ln(4^3) = 3*ln(4) = 3*1.386 = 4.158.

These properties are useful in simplifying and solving logarithmic equations involving natural logarithms.

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