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2 years ago

Udlinius6x – 12 = 6(x - 2)

Mathematics

1 answer:

Sunny_sXe [5.5K]2 years ago

5 0

If you distribute the 6(x-2) you would get 6x-12 so zero would equal zero

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If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

2 years ago

Help me solve this problem please

ICE Princess25 [194]

Answer:

actually what is this is you is this a geometry, trigonometry I don't know what to call

8 0

2 years ago

Point F' corresponds to point D. point E'. point F. point E.

Zepler [3.9K]

Answer:

F' corresponds to point F

Step-by-step explanation:

When a point is the result of some transformation, we often designate that result using the base name of the original, with a prime (') added. In this case, we expect that F' is the transformation of point F.

<em>Comment on point naming</em>

Of course, points can be given any name you like. These conventions are adopted to aid in communication about transformations and correspondence between points. It would be unusual--even confusing, but not unreasonable, for point F' to correspond to point D, for example. In the case of certain transformations, point F' may actually <em>be</em> point D.

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2 years ago

A student theater charges $9:50 per ticket. The theater has already sold 70 tickets. Write and solve an inequality that represen

kipiarov [429]

70 x 9.50 = 665 so 1000 - 665 =335 and 335 / 9.50 = 35 so, it needs 35 more tickets to get 1000.

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3 years ago

If one yard equals 3 ft in one mile equals 5280 ft how many yards are there in 2 miles

Georgia [21]

Answer:

2 miles = 3520 yards

Step-by-step explanation:

1 mile = 1760 yards

2 miles = 3520 yards

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3 years ago

Udlinius6x – 12 = 6(x - 2)​

Udlinius6x – 12 = 6(x - 2)