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Andrew [12]
2 years ago
11

Use the properties of logarithms to expand the expression as a sum or difference, and/or constant multiple of logarithms. (Assum

e all variables are positive) ​

Mathematics
1 answer:
Alecsey [184]2 years ago
6 0

Answer:

\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)

Step-by-step explanation:

\log_5(\frac{9\sqrt{x}}{y^3})

First rule I'm going to use is the quotient rule:

\log_b(\frac{m}{n})=\log_b(m)-\log_b(n)

\log_5(9\sqrt{x})-\log_5(y^3)

Secondly, I'm going to rewrite the radical.

\sqrt{x}=x^\frac{1}{2}

\log_5(9x^\frac{1}{2})-\log_5(y^3)

Third, I'm going to use the product rule on the first term:

\log_b(mn)=\log_b(m)+\log_b(n)

\log_5(9)+\log_5(x^\frac{1}{2})-\log_5(y^3)

Fourth, I'm going to use power rule for both of the last two terms:

\log_b(m^r)=r\log_b(m)

\log_5(9)+\frac{1}{2}\log_5(x)-3\log_5(y)

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Let:

k\cdot IW=I^{\prime}W^{\prime}

Where:

k = scale factor

IW = 12

I'W'= 8

so, solving for k:

\begin{gathered} k=\frac{I^{\prime}W^{\prime}}{IW} \\ k=\frac{8}{12}=\frac{2}{3} \end{gathered}

3 0
1 year ago
What is an equation of the line that passes through the point (−3,−1) and is perpendicular to the line x-2y=6?
gogolik [260]

Answer:

y = 2x+5

Step-by-step explanation:

rearrange the equation to make y the sof

y = 1/2x - 3

to find gradient of perpendicular line

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5 0
2 years ago
What is the total amount in an investment of $3500 that was compounded quarterly for 8 years at a rate of 5%?
erica [24]

Answer:

Principal = 3500

Time = 8 years

We are given that compound quarterly

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Substitute the values :

A=3500(1+\frac{0.05}{2})^{2 \times 2}

A=3863.345

Interest = 3863.345 - 3500 = 363.345

Hence the total amount in an investment of $3500 that was compounded quarterly for 8 years at a rate of 5% is $3863.345 and the interest that was made on that account mentioned is $363.345

8 0
3 years ago
If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?
algol [13]

Answer:

<u>Statements (1) and (2) TOGETHER are NOT sufficient.</u>

Explanation:

As in the equation (327)(510)(z) = (58)(914)(xy) there are THREE variables in total i.e. "x", "y" and "z" hence minimum three equations are required to find out values of all variables. Hence,

If the given number of equations is equal to total variable used in any of the equation, values of all the variables can be find out otherwise there can be unlimited number of solutions.

So, value of "x" cannot be determined with the given data.

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3 years ago
Les gusta mi dibujo soy nueva
maksim [4K]

Answer:

Si, es muy bueno!

Step-by-step explanation:

4 0
1 year ago
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