Question

WRITE THE EXPRESSION AS A SINGLE LOGARITHM WITH THE COEFFICIENT IS 1. 10LOG(X+7)+3LOG(X-1)-7LOG(X-2)

Answer 1

\[10*log{(x+1) + 3*log{(x-1)} - 7 *log{(x-2)}} \]

Answer 2

we can review rules of logarithms, \[a*log{(b)} = log{(b^a)}\]

Answer 3

so, let's apply this to each part of the equation: \[\log{((x+1)^{10})} +log{((x-1)^3}) - log{((x-2)^7)} \]

Answer 4

and another rule: \[log(a) - log(b) = log(a/b)\]

Answer 5

and \[log(a) + log(b) = log(a*b)\]

Answer 6

so we can condense this: \[\log{((x+1)^{10})} +log{((x-1)^3}) - log{((x-2)^7)}\] using those rules

Answer 7

would you like to give it a try?

Answer 8

What did you get for the final answer?

Answer 9

I haven't worked out that far

Answer 10

what did you get?

Answer 11

I GOT -4 THATS WRONG

Answer 12

OK, just apply the rules of multiplying and dividing logarithms and you'll get the final answers, just 2 more steps are left

Answer 13

I TRIED

Answer 14

ok, let's look at the first two terms then

Answer 15

because they are being added together, then we can use the multiplication rule

Answer 16

of logarithms

Answer 17

\[\log{((x+1)^{10})} +log{((x-1)^3})\] should now be of the form \[log(a*b)\]

Answer 18

sorry

Answer 19

\[log((x+1)^{10} * (x-1)^3)\]

Answer 20

so you have now: \[log((x+1)^{10} * (x-1)^3) - log((x-2)^7)\]

Answer 21

we apply the rule of division: \[log(a)-log(b) = log(a/b)\]

Answer 22

\[log((x+1)^{10} * (x-1)^3) - log((x-2)^7)\] now is \[log(\frac{(x+1)^{10} * (x-1)^3}{(x-2)^7})\]

Answer 23

there you have it

Answer 24

so, you got -4?