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3 years ago

Expand a logarithmic expression

Mathematics

2 answers:

ivanzaharov [21]3 years ago

8 0

The logarithmic expression is

$log (\sqrt{z^5}/(x^3y))$

To expand the expression we have to use some properties of logarithm.

We know that $log(m/n) = log (m) - log(n)$

By using this property we can write,

$log(\sqrt{z^5}) - log(x^3y)$

Square root means to the power 1/2, so for $\sqrt{z^5}$ , we can write $z^(5/2)$ .

$log(z^(5/2)) - log(x^3y)$

Now we have to use another property of logarithm.

We know that, $log(mn) = log(m) + log(n)$

So we will use this property to $log(x^3y)$

$log(z^(5/2)) - log(x^3y)$

$log(z^(5/2)) - (log(x^3) + log(y))$

$log(z^(5/2)) - log(x^3) - log(y)$

Now we have to use another property of logarithm.

We know that, $log(a^m) = m log(a)$

By using this property we can write,

$(5/2)log(z) - 3log(x) - log(y)$

This is the required aswer here.

irinina [24]3 years ago

7 0

we have logarthmic division function .

$log(\frac{\sqrt{z^5}}{x^3y} )$

we know that $log(a/b)=log a-log b$

so the given function will be $log(\sqrt{z^5} )-log(x^3y)=\frac{5}{2} logz-(3logx+logy)$

we know that if a exponent in log is bought down it will be multiplied with log

so we got square root of z^5 and x^3 as 5/2 and 3 .

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Please help another assignment I’m not very good at math !!

juin [17]

Answer:

Prime Factorization of 576

$576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

Prime Factorization of 64

$64=2\times 2\times 2\times 2\times 2\times 2$

The Expression in simplest form is

$\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}$

Step-by-step explanation:

Simplify:

$\sqrt{\dfrac{576}{64} }$

Now,

Prime Factorization of 576

$576=2\times 288\\576=2\times 2\times 144\\576=2\times 2\times 2\times 72\\576=2\times 2\times 2\times 2\times 36\\576=2\times 2\times 2\times 2\times 2\times 18\\576=2\times 2\times 2\times 2\times 2\times 2\times 9\\576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$

Prime Factorization of 64

$64=2\times 32\\64=2\times 2\times 16\\64=2\times 2\times 2\times 8\\64=2\times 2\times 2\times 2\times 4\\64=2\times 2\times 2\times 2\times 2\times 2$

Now,

$\sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2} }\\ \sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{3\times 3}{1}}\\\therefore \sqrt{\dfrac{576}{64} }=3$

The Expression in simplest form is

$\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}$

8 0

3 years ago

A ballpark sells bags of popcorn for $1 each and bags of peanuts for $2 each. Hector will buy x bags of popcorn and y bags of pe

Rasek [7]

Answer:

Hector will buy 6 peanut bags and he will buy 2 ppopcorn bags

Step-by-step explanation:

He will buy 6 bags of peanuts because that will be 12$ and he will buy 2 popcorn bags because it will be 2$. He only wanted to buy 8 bags of snacks and he only wanted to spend 14$. Hope this helps!!! :)

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3 years ago

The opposite of 10/7

ch4aika [34]

I am not sure want you want. But I'll give you both the reciprocal and opposite of 10/7.

Reciprocal of 10/7 is 7/10

Opposite of 10/7 means to put a negative if it is positive and take away the negative if it already negative.

Opposite of 10/7 is -10/7.

8 0

3 years ago

Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right. 1. x2 − 7x

just olya [345]

Answer:

1. ---> d. Prime

2.---> c. (x-4)(x+3)

3.---> a. (x-6)(x+2)

4. ---> b. (x-2)(x+6)

Step-by-step explanation:

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial $ax^2+bx+c$ multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as $(x-/+ number)(x-/+number)$ .