A box contains 3 items that are labeled a, b, and

Condense the following logarithm: 5log_4(a) - 6log_4(b)

grin007 [14]

Hi there! We are given the expression:

$\large \boxed{5 log_{4}(a) - 6 log_{4}(b) }$

To condense or simplify the following logarithm. You have to remember these properties:

Properties - Logarithm

$\large{ log_{b}(a)^{n} = n log_{b}(a) } \\ \large{ log_{b}(a) - log_{b}(c) = log_{b}( \frac{a}{c} ) }$

These two properties are what we need for our problem. Therefore,

$\large{ log_{4}(a)^{5} - log_{4}(b)^{6} }$

We use the log_b(a)^n = nlog_b(a) property to convert in the form above. Next, we use the second property.

$\large{ log_{4}( \frac{ {a}^{5} }{ {b}^{6} } ) }$

Answer

log base 4 of (a^5/b^6) is our simplifed form.

Any questions can be asked through comment as I may reply soon. Thanks for using Brainly! Have a good day and happy learning! :)

6 0

2 years ago

Devaughn is 14 years older than Sydney. The sum of their ages is 110. What is Sydney's age?

Monica [59]

D = s-14
d+s = 76

• substitution;
(s-14)+s = 76
2s-14= 76
2s = 90
s = 45 years old for Sydney
d = s-14 = 31 years old for Devaughn
hope this helps

4 0

2 years ago

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Rachel has taken 6 tests so far and has received scores of 83%, 92%, 79%, 88%, 89%, and 95%. What must Rachel receive on her sev

Vinil7 [7]

Let the score on her seventh test be "x".

SO,

$\frac{83+92+79+88+89+95+x}{7} =90\\\\ \frac{526+x}{7}=90\\\\ 526+x=630\\\\x=630-526\\\\ \boxed{x=104}$

∴ He must get 104% on his seventh test to get an average score of 90%

5 0

2 years ago

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A bus covers 270km distance in 6 hours.

pentagon [3]

Answer:

(i)= 45 KPH, (ii) = 251 miles

Step-by-step explanation:

'Per' essentially means divide. Thus, to find Kilometres per hour, divide 270 by 6= 45. The bus is travelling at 45 KPH.

Then, to see how far a nine hour trip would cover, distance = speed * time = 251 miles.

7 0

1 year ago

I'm learning about Equivalent systems of equations, please help!

kobusy [5.1K]

OK to solve this, we have to solve each system presented through elimination or substitution and find which one is equivalent to that of the teacher's!

First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y
$x= \frac{10-5y}{-2}$
Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6

Substitute in x
x= -10-5(-6)/2
x=-20

TEACHER'S ANSWER (-20,-6)

GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11

x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)

SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)

-5x+14y=16
-5x=16-14y
x=(16-14y)/-5

-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60
48-42y+45y=60
48+3y=60
3y=12
y=4

x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)

So neither Goku or Selina got the same answer as the teacher

3 0

2 years ago

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