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Mnenie [13.5K]
4 years ago
10

Solve: 3 ln x = ln 216

Mathematics
2 answers:
BaLLatris [955]4 years ago
3 0

3\ln x=\ln 216\\ \ln x^3 =\ln 216\\ x^3=216\\ x=6

ella [17]4 years ago
3 0

To solve this problem, first we must understand that the coefficient of a log can also be expressed as the exponent of the argument. If we know this property, we can rewrite the equation as follows:


ln x^3 = ln 216


Next, we must use the inverse operation of ln to get rid of the logs on both sides. Because ln is really just a log with base e, if we make both sides of the equations the exponents of a base e, this will cancel the lns, and leave us with a simple equation.


e^ln(x^3) = e^ln216


This leaves us with:


x^3 = 216


If we take the cube root of each side to cancel out the degree 3 exponent on the variable x, we get that the answer is: x = 6 (Note: -6 is not an acceptable answer because (-6)^3 is actually -216).


Hope this helps!

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Nesterboy [21]

Answer:

The mixture C is the correct option

Step-by-step explanation:

According to the given scenario, the calculation is as follows:

For Mixture A

Blue Paint - 5 cups

White Paint - 12 cups

The ratio between them is 5:12

For Mixture B

Blue Paint - 6 cups

White Paint - 6 cups

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It came by multiply the numerator and denominator by 12

For Mixture C

Blue Paint - 4 cups

White Paint - 12 cups

 The ratio between them is 4:12

For Mixture D

Blue Paint - 5 cups

White Paint - 6 cups

 The ratio between them is 5:6 = 10:12

It came by multiply the numerator and denominator by 12

As it can be seen that in all four mixtures the denominator is the same so for calculating the lowest ratio we have to see the small value in the numerator

As it can be seen that there is a small value of 4

hence, the mixture C is the correct option

5 0
3 years ago
Read 2 more answers
A perfect square ends with the same two digits. How many possible values of this digit are there?
Alex73 [517]

Answer:

A perfect square is a whole number that is the square of another whole number.

n*n = N

where n and N are whole numbers.

Now, "a perfect square ends with the same two digits".

This can be really trivial.

For example, if we take the number 10, and we square it, we will have:

10*10 = 100

The last two digits of 100 are zeros, so it ends with the same two digits.

Now, if now we take:

100*100 = 10,000

10,000 is also a perfect square, and the two last digits are zeros again.

So we can see a pattern here, we can go forever with this:

1,000^2 = 1,000,000

10,000^2 = 100,000,000

etc...

So we can find infinite perfect squares that end with the same two digits.

7 0
3 years ago
Please help me with this question
lianna [129]

Answer:

Step-by-step explanation:

3 0
3 years ago
Please help me with my math question<br> Will give brainliest <br> Brainliest!!!!
DiKsa [7]

Answer:

12x - 6

Step-by-step explanation:

8x - 3 + 4x - 3

12x - 6

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6 0
3 years ago
Read 2 more answers
Janet deposited $9,600 into an account that pays 4.4 interest, compounded daily. At the end of nine months, how much interest ha
neonofarm [45]

bearing in mind that 9 months is not even a year, but since there are 12 months in a year, then 9 months is really 9/12 years.


\bf ~~~~~~ \stackrel{\textit{daily}}{\textit{Continuously}} \textit{Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9600\\ r=rate\to 4.4\%\to \frac{4.4}{100}\dotfill &0.044\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ A=9600e^{0.044\cdot \frac{3}{4}}\implies A=9600e^{0.033}\implies A\approx 9922.09 \\\\\\


\bf \stackrel{\textit{interest earned}}{9922.09-9600\implies 322.09}

5 0
3 years ago
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