Question

Use the rules of logarithms to expand
log[(x+3)^4(x-5)^7]

Answer 1

Like this?
\[\log[(x+3)^{4(x-5)^7}]\]

Answer 2

\[LOG[(x+3)^{4} (x-5)^{7}]\]

Answer 3

I should of posted my question and then wrote that out :P

Answer 4

use the following 2 rules

log ab = log a + log b
and
log a^n = n log a

Answer 5

@welshfella are you saying this\[\log (ab)=\log (x+3)^{4} +\log(x-5)^{7}\]

Answer 6

okay, that makes things easier.
\[\log[(x+3)^4(x-5)^7]\]
You see, most of the times we want to expand a logarithmic math expression we use the properties of the logarithm.
In this case we will use a logarithmic property that involves the product of the internal logarithmands.
\[\log_{n} AB=\log_{n} A + \log_{n}B \]
Well, in the case of this excercise we can apply it, since the base is 10:
\[\log[(x+3)^4(x-5)^7]\]
\[\iff \log (x+3)^4+\log(x-5)^7\]
This of course is not ready yet, because we still have those exponents, from that we will use the property:
\[\log_{n} A^m = m(\log_{n} A)\]
So, we can take down those exponents by using this property, which comes in quite useful when dealing with logarithms:
\[ \log (x+3)^4+\log(x-5)^7\]
\[\iff 4\log(x+3)+7\log(x-5)\]

Answer 7

you are on the way to answering it
now you apply the second rrule

Answer 8

OwlCoffee has it

Answer 9

@welshfella Ah you started and then @Owlcoffee finished. I saw where you were going, it was a matter of taking the exponents after you got it into the first form! So simple..

Answer 10

@Owlcoffee I will medal you, can you medal @welshfella

Answer 11

yes Not difficult

Answer 12

@welshfella Thank you!! :)

Answer 13

yw

Answer 14

I put in the right answer though with my image right?