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I have a log problem that deals with properties of logarithms picture included

I have a log problem that deals with properties of logarithms picture included-example-1

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The Properties of Logarithms are shown below:

• a)

To rewrite the first logarithm, we have to remember that:


(3)/(4)=0.75

Therefore, we can rewrite the expression as follows:


\log _a(0.75)=\log _a((3)/(4))

Using the property of division of the logarithms we get:


=\log _a((3)/(4))=\log _a(3)-\log _a(4)

Replacing the given values:


=0.62-0.78=-0.16

• b)

Also, if we multiply 3 times 4 we get 12. Thus, we can rewrite the second expression:


\log _a(12)=\log _a(3*4)

Using the multiplication property of the logarithm:


=\log _a(3*4)=\log _a(3)+\log _a(4)

Replacing the values:


=0.62+0.78=1.4

• c)

Finally, for the last expression we have to remember that a square root can also be written as an exponent:


\log _a(\sqrt[]{3})=\log _a(3^{(1)/(2)})

Then, using the exponentiation property of the logarithms we can rewrite that last expression:


=\log _a(3^{(1)/(2)})=(1)/(2)\log _a(3)

As we already know the value of loga(3), we can just replace it and get the result:


=(1)/(2)\cdot0.62=0.31

Answer:

• a) -0.16

,

• b) 1.4

,

• c) 0.31

I have a log problem that deals with properties of logarithms picture included-example-1
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