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Alex17521 [72]
3 years ago
7

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

ultipal of logarithms.See example 3.
In 3x(x + 1)/(2x + 1)^2
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0

Answer:

\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}

Step-by-step explanation:

we need to keep in mind two properties of log:

  • \ln{ab}=\ln{a}+\ln{b}
  • \ln{\dfrac{a}{b}}=\ln{a}-\ln{b}
  • \ln{a^b}=b\ln{a}

\ln{\dfrac{3x(x+1)}{(2x+1)^2}}

\ln{\left(\dfrac{3x(x+1)}{(2x+1)^2}\right)}\\\ln{(3x(x+1))}-\ln{((2x+1)^2)}\\\ln{(3x)}+\ln{(x+1)}-\ln{((2x+1)^2)}

\ln{(3x)}+\ln{(x+1)}-2\ln{(2x+1)}

this is the rewritten expression!

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The angle of elevation to the top of a water tower from point A on the ground is 19.9°. From point B, 50.0 feet closer to the to
zepelin [54]

Answer:

Answer in terms of a trigonometric function :

h = \frac{20tan(19.9)}{0.4-tan(19.9)}

Answer in figures

h = 190.5 feet

Step-by-step explanation:

Consider the sketch attached below to better understand the problem.

Let x be the distance between point B and the base of the water tower.

tan (19.9)=\frac{h}{50+x} ---------------equation 1\\

tan (21.8)=\frac{h}{x}----------------equation 2

From equation 2,

x =\frac{h}{tan21.8}=\frac{h}{0.4}

substituting the value of x into equation 1, we get

tan (19.9)=\frac{h}{50+(\frac{h}{0.4} )}

tan 19.9=h\times \frac{0.4}{20+h}

cross multiplying,

20\times tan(19.9) +htan(19.9)=0.4h

20tan(19.9)= h(0.4-tan(19.9))

h= \frac{20tan (19.9)}{0.4-tan (19.9)}

The height of the tower is h= \frac{20tan (19.9)}{0.4-tan (19.9)} in terms of the trig function "Tan"

The equation can simply be evaluated to get the answer in figures since the angles are given in the question

5 0
3 years ago
−2/3(3 - 1/2)(-1) = ?
chubhunter [2.5K]

The correct answer would be <u><em>B. 2 - 1/3</em></u>

8 0
3 years ago
kyle drew tree line segments with these lenngths: 2/4" , 2/3" , 2/6" list the fractions in order from least to graiter
exis [7]
First you find a common denominator, which is 12 ( as 4,3 and 6 all go into 12). So 2/4 becomes 6/12, as 4 multiplied by 3 is 12 and whatever you do to the denominator you must do to the numerator. Then 2/3 becomes 8/12. And 2/6 becomes 4/12. If you put these in order the answer is:

2/6, 2/4, 2/3

6 0
3 years ago
It wants me to find the degree of FJE and FJH but these confuse me
ELEN [110]
Here, EJI + FJE = 180    [ Linear-Pair Equation ]
FJE + 135 = 180
FJE = 180 - 135
FJE = 45

Now, FJH + FJE = 180  [Linear-Pair Equation ]
FJH + 45 = 180
FJH = 180 - 45
FJH = 135

Hope this helps!
8 0
3 years ago
What term can you add to 5/6x -4 to make an equivalent to 1/2x-4
solmaris [256]

Answer:

Denote adding term = a

a = (5/6x) - 4 - (1/2x) - 4

a = (5/6x) - (1/2x)

a = (5/6x) - (3/6x)

a = (2/6x)

a = (1/3x)

*******************************

a = (5/6)x - 4 - (1/2)x - 4

a = (5/6)x - (1/2)x

a = (5/6 - 1/2)x

a = (1/3)x

Hope this helps!

7 0
3 years ago
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