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3 years ago

Write log4 14 as a logarithm of base 3. HELP!!!!!

Mathematics

2 answers:

harkovskaia [24]3 years ago

8 0

Answer:

$\log_414=\frac{\log_{3}14}{\log_{3}4}$

Step-by-step explanation:

We have given $log_4 14$ is given we need to convert it in logarithmic base 3

Using log base change property

$\log_ab=\frac{\log_cb}{\log_ca}$

So, here we have to change $log_4 14$ using log base change property with base 3

where, a=4,b=14 and c=3

Substituting these values in log base change property and we get

Therefore, $log_4 14=\frac{\log_{3}14}{\log_{3}4}$

Sonja [21]3 years ago

3 0

It would be log3 14/log3 4
Hope this helps. (:

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3 years ago

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The region bounded by y=(3x)^(1/2), y=3x-6, y=0

Ganezh [65]

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is $y = (3x)^{\frac{1}{2} }$

⇒ $y^{2} = 3x$ ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

$y^{2} - y - 6 = 0$

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = $\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx$

= $\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}$

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3 years ago

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3 years ago

What is the fraction twelve twentieths in its simplest form

Alla [95]

You mean $\frac{12}{20}$ or $\frac{20}{12}$ ?

If you had meant, $\frac{12}{20}$ , then the simplest form of this fraction would be - $\frac{3}{5}$

Divide both parts of the fraction by 4, and you get $\frac{3}{5}$ the simplest form of the fraction.
Finding out the simplest form of a given fraction is nothing else than cancelation.

Flop it, you have with you - $\frac{20}{12}$
Flop the simplest form of the previous fraction, that's $\frac{5}{3}$

If you had meant $\frac{20}{12}$ , then this will certainly be of any use to you.

HOW TO UNDERSTAND THAT THE FRACTION IS IN ITS SIMPLEST FORM?
Maybe, you are just simplifying and simplifying...but you don't even know when to stop. You can understand whether a fraction is in its simplest form or not by seeing that the numerator and the denominator have a common factor to divide it by, or not.

For instance, consider the case here - $\frac{3}{5}$ or $\frac{5}{3}$ <span>. We can't divide it any further. So, we know that it is in its simplest form.
</span>
L O N G Process:
Well, if you want to divide it by the smallest common factor to its larger, then --
$\frac{12}{20}$ or $\frac{20}{12}$

1) Divided by 2 = $\frac{6}{10}$ or $\frac{10}{6}$

2) Next, also by 2 = $\frac{3}{5}$ or $\frac{5}{3}$

That took much longer, right.<span> So, it is more preferable to divide the fraction by the possible largest common factor, you can guess of.</span>

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