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3 years ago

If (x+y)^2=125xy,show that, 2 log (x+y) = 3 log 5+log x+ log y

Mathematics

1 answer:

Brums [2.3K]3 years ago

7 0

Formulas used :

$loga^ x = x \ log a$

$logab = log a + logb$

Steps :

$(x+y)^2 = 125xy\\\\log(x+y)^2 = log(125xy)\\\\2log(x+y) = log 125 + log x + log y\\\\2log(x+y) = log 5^3+ log x + log y\\\\2log(x+y) = 3 log 5 + log x + log y\\\\$

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VikaD [51]

Answer:

9/2 if n goes to infinity and that the 2n^3 is under the whole expression

Step-by-step explanation:

Let me clear this .

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Did I put the parentheses in the right spot?

because if you leave it the way you did, then the whole expression goes to positive infinity as n goes to infinity But I will do this with parentheses

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= (9/2) + 0 - 0

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In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

Maksim231197 [3]

Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

$x+y\le 180$

3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$