Mathematics, 07.10.2019 14:30 den14

Which expression is equivalent to log8 4a (b-4/c4)?

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Answer from: emmalucilleblaha1995

The
the main rules of the use of logarithm are

loga[a] = 1
loga[AxB] =loga[A] +loga[B] for all value positive of A and B
loga[A/B] = loga[A] - loga[B] for all value positive of A and B

in our case, log8 4a (b-4/c4)

so it is equivalent to log8 4a + log8(b-4/c4)
and since loga[A/B] = loga[A] l - oga[B] , log8(b-4/c4) =log8(b-4) - log8(c4)

the possible expression:

log8 4a (b-4/c4) = log8 4a + log8(b-4) - log8(c4)

Answer from: Kazya4

The equivalent expression of the given logarithmic expresson is 1+log_8a+log_8 (b-4)-log_8 2c^4 .

The given expression is log_8 [4a ((b-4)/c^4)] .

Use the basic rules of logarithm to find the equivalent expression.

$log_aa=1\\log(ab)=loga+logb\\log(a/b)=loga-logb\\loga^b=bloga$

Solve the given expression as,

$log_8 [4a ((b-4)/c^4)]=log_8 [8a ((b-4)/2c^4)]\\=log_8 8+log_8a+log_8 (b-4)-log_8 2c^4\\=1+log_8a+log_8 (b-4)-log_8 2c^4$

Therefore, the equivalent expression of the given logarithmic expresson is 1+log_8a+log_8 (b-4)-log_8 2c^4 .

For more details, refer to the link:

link

Answer from: Quest

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

Answer from: Quest

the answer is b

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