Use the properties of logaritms to expand the expression

It's like writing 2x + x. 3. In the first line of your work, you have "in(x-7)". Again, I think you're treating the "in" as a number, and it's not.
  • #1
pooker
16
0

Homework Statement



IN * ((4x^5 - x -1)(square root x-7)) / (x^2 + 1)^3





The Attempt at a Solution



in(4x^5 - x - 1) + in(square root x-7) - in(x^2 + 1)^3

in(4x^5 - x - 1) + 1/2in(x-7) - 3in(x^2 +1)

5in4x - inx - 1 + 1/2(inx -in7) - 3 (2inx + in)


I know that's not right but its all I can think of at the moment.
 
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  • #2
pooker said:

Homework Statement



IN * ((4x^5 - x -1)(square root x-7)) / (x^2 + 1)^3





The Attempt at a Solution



in(4x^5 - x - 1) + in(square root x-7) - in(x^2 + 1)^3

in(4x^5 - x - 1) + 1/2in(x-7) - 3in(x^2 +1)

5in4x - inx - 1 + 1/2(inx -in7) - 3 (2inx + in)


I know that's not right but its all I can think of at the moment.

First off, it's not in, it's ln (ell en), short for logarithm naturalis or something close to that. Before being able to help you out, can you confirm that this is the problem?
[tex]ln \frac{(4x^5 - x - 1)(\sqrt{x - 7})}{(x^2 + 1)^3}[/tex]

If so, then an expression of the form ln[(AB)/C] can be rewritten as ln A + ln B - ln C.
Then because the individual expressions B and C have exponents, you can use the property of logarithms that ln a^b = b ln a.

Mistakes in your work:
1. You start with IN *. I've already mentioned that it is LN, but the mistake here is the mulitiplication symbol. ln is a function, not a number, so it's meaningless to think of using it to multiply.
2. In your later work you have "3in(x^2 +1)" and in the next line you have "3 (2inx + in)". This suggests to me that you think that "in" is a number. It's not. 2 inx + in is meaningless.
 

1. What are the properties of logarithms?

The properties of logarithms are rules or formulas that are used to manipulate logarithmic expressions. These properties include the product rule, quotient rule, power rule, and change of base rule.

2. How do you expand a logarithmic expression using properties?

To expand a logarithmic expression, you can use the properties of logarithms to rewrite the expression as a sum, difference, or product of simpler logarithms. For example, the product rule states that logb(xy) = logb(x) + logb(y).

3. Can you explain the product rule of logarithms?

The product rule of logarithms states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers. This can be written as logb(xy) = logb(x) + logb(y). This property can be useful when dealing with multiplication inside a logarithm.

4. How is the quotient rule used in expanding logarithmic expressions?

The quotient rule of logarithms states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers. This can be written as logb(x/y) = logb(x) - logb(y). This property is useful for dealing with division inside a logarithm.

5. What is the change of base rule for logarithms?

The change of base rule for logarithms states that any logarithm with a base b can be rewritten as a logarithm with a different base a by using the following formula: logb(x) = loga(x) / loga(b). This rule is helpful when calculating logarithms with bases other than the common bases of 10 and e.

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