Question

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

Answer 1

alright familiar with the log rules ?

Answer 2

not really. I'm new to them!

Answer 3

quotient rule\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\]
to expan you can change division to subtraction
product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\]
addition <----> multiplication

power rule \[\large\rm log_b x^y = y \log_b x\]

Answer 4

expand*

Answer 5

whoa. Okay.

Answer 6

that's confusing. :(

Answer 7

so which rule would you apply first ?

Answer 8

\[\log[(x+3)^4 (x-5)^7] \] is same as \[\log[(x+3)^4* (x-5)^7] \]

Answer 9

okay, which one is easier?

Answer 10

what do you mean ??

Answer 11

quotient rule\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\]
to expan you can change division to subtraction
product rule \[\large\rm log_b x + \log_b y = \log_b( x \times y )\]
addition <----> multiplication
first you should apply one of these rule

Answer 12

there is a multiplication sign in the equation so would you apply product rule or quotient rule ?

Answer 13

okay sorry how do i do that?

Answer 14

i have no idea tbh

Answer 15

here is an example \[\log (x *2) \rightarrow \rm expand ~~~\log (x) + \log(2)\]
it was multiplication to expand i changed it to addition

Answer 16

\[\log[(x+3)^4* (x-5)^7] \] how would you split it into two logs ?

Answer 17

x+3^4 then x-5^7 ?

Answer 18

ye but what sign would be in between (x+3)^4 and (x-5)^7

Answer 19

\[\log (\color{ReD}{x} \color{green}{*}\color{blue}{2}) \rightarrow \rm expand ~~~\log (\color{ReD}{x}) \color{green}{+} \log(\color{blue}{2})\]
mybe colors help u to understand these :=)

Answer 20

*? or +?

Answer 21

im sorry, im trying!! :(

Answer 22

\[\log (\color{ReD}{(x+3)^4} \color{green}{*}\color{blue}{(x-5)^7}) \]

Answer 23

*(multiplication sign like x )

Answer 24

since there is a multiplication sign you should convert it to addition (+ sign )

Answer 25

so log(x+3)^4 + (x-5)^7 ? @Nnesha

Answer 26

no we should split it into two logs...
\[\large\rm \color{reD}{ \log}(x+3)^4 +\color{Red}{log} (x-5)^7 \]

Answer 27

now apply the power rule

Answer 28

power rule \[\large\rm log_b x^\color{ReD}{y} = \color{reD}{y} \log_b x\]

Answer 29

I'm seriously SO confused right now.. @Nnesha

Answer 30

what part you don't understand ???

Answer 31

here is an example \[\rm \log x^\color{Red}{2}\] would be \[\rm \color{Red}{2} logx\]

Answer 32

just move the exponent at front of the log

Answer 33

so .. 4logx?

Answer 34

well the example i gave u there base is just `x` what's the base in your question ?

Answer 35

here is another example \[\large\rm \log (x)^\color{Red}{a} + \log (y)^\color{reD}{z} \rightarrow ~~~\color{red}{a}log(x) + \color{Red}{z}log(y)\]

Answer 36

I don't understand any of this. i don't even know what to do.

Answer 37

there any 3 rules to expand log
\[\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}\]\[\large\rm log_b x + \log_b y = \log_b( x \times y )\]\[\large\rm log_b x^y = y \log_b x\]

that's it

Answer 38

look at 2nd rule
\[\large\rm \color{Red}{\log}( x \times y )=\color{ReD}{log}~(x) + \color{red}{log}{(y)}\]

in other words distribute parentheses by log and then just change the multiplication sign by + sign