All categories

2 years ago

To find the result when

Mathematics

1 answer:

Liula [17]2 years ago

5 0

Answer:

answer is 51 hope i'm corret

You might be interested in

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

3 years ago

Estimate the sum of the decimal below by rounding to the nearest whole number.

Marizza181 [45]

The non-rounded sum is 15.579, so you’d round up to 16 since 5 and up rounds up. Hope this helps<3

4 0

3 years ago

What is the value of x in this triangle?

Vadim26 [7]

Answer: 5 pls44444444 do you want my ps5

Step-by-step explanation:

8 0

2 years ago

The two different types of cells are please tell me the answer

vodomira [7]

Answer:

eukaryotic cells (cells that have a nucleus) and prokaryotic cells (cells that do not have a nucleus)

Step-by-step explanation:

5 0

3 years ago

7 - r/8 - 3d Variables r=32 and d= 2

satela [25.4K]

The required value if r = 32 and d = 2 is -3

Given the expression

$7-\frac{r}{8} - 3d$

Substituting the given variables

r = 32

d = 2

The expression becomes

$= 7-\frac{32}{8} - 3(2)\\= 7 - 4 - 6\\= 3 - 6\\= -3$

Hence the required value is -3

Learn more here: brainly.com/question/17499155

6 0

2 years ago