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Ki-nana18
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Homework Statement
Use the properties of logarithma to xpand the logarithmic function ln[(x2+1)(x-1)]
Homework Equations
The Attempt at a Solution
[ln x2+ln 1]+[ln x-ln 1]
2 ln x+ln x
Is the something else you're thinking about factoring x^2 + 1?gamer_x_ said:the first step makes sense: [tex]ln[(x^2+1)(x-1)]=ln(x^2+1)+ln(x-1)[/tex]
but then you continued: [tex]ln(x^2+1)=ln(x^2)+ln(1)[/tex]
You can't do that, but you can do something else to the [tex]x^2+1[/tex]...
The basic properties of logarithms include the product rule, quotient rule, and power rule. The product rule states that the logarithm of a product is equal to the sum of the logarithms of each factor. The quotient rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. The power rule states that the logarithm of a power is equal to the product of the power and the logarithm of the base.
To use the product rule to expand a logarithmic function, first identify each factor in the product. Then, apply the product rule by taking the logarithm of each factor and adding them together. This will result in the expanded logarithmic function.
The quotient rule for logarithms states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. In other words, to expand a logarithmic function with a quotient, you can subtract the logarithm of the denominator from the logarithm of the numerator.
To expand a logarithmic function with a power using the power rule, simply multiply the power by the logarithm of the base. This will result in an expanded logarithmic function with the power as the coefficient.
Yes, there are a few other properties of logarithms that can be used to expand a logarithmic function. These include the change of base formula and the logarithm of a reciprocal rule. The change of base formula allows you to rewrite a logarithm with a different base, while the logarithm of a reciprocal rule states that the logarithm of a reciprocal is equal to the negative of the logarithm of the original number. These properties can be useful when expanding more complex logarithmic functions.