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2 years ago

What is m∠C? Enter your answer in the box. m∠C= °

Mathematics

1 answer:

serious [3.7K]2 years ago

5 0

Answer:

m∠C = 60°

Step-by-step explanation:

First, let's start with the fact that all angles in a triangle add up to 180°. That means that:

x+3x+2x=180°

We can simplify it into:

6x=180°

To figure out x, we need to divide 180 by 6.

That means each x is 30°

m∠C = 2x

m∠C = 60°

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The logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

<h3>Simplifying Logarithms</h3>

From the question, we are to write the given logarithm expression as a sum or difference of logarithms

The given logarithm is

$log_{4 }6ab$

This can be written as

$log_{4 }6 \times a \times b$

From one of the rules of logarithm, we have that

$log_{x }yz= log_{x }y + log_{x }z$

Thus,

$log_{4 }6 \times a \times b$ becomes

$log_{4 }6 + log_{4 }a + log_{4 }b$

This can be further simplified into

$log_{4 }3 \times 2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + log_{4 }2 + log_{4 }a + log_{4 }b$

If desired, this can be further simplified into

$log_{4 }3 + log_{2^{2} }2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} log_{2}2 + log_{4 }a + log_{4 }b$

$log_{4 }3 + \frac{1}{2} (1)+ log_{4 }a + log_{4 }b$

$\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Hence, the logarithm written as a sum of logarithm and simplified as much as possible is $\frac{1}{2} +log_{4 }3 + log_{4 }a + log_{4 }b$

Learn more on Simplifying logarithms here: brainly.com/question/17851187

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