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Mila [183]
3 years ago
9

URGENT HELP ME PLEASE

Mathematics
1 answer:
Trava [24]3 years ago
5 0

Answer:

(a)\log_3(\dfrac{81}{3})=3

(b)\log_5(\dfrac{625}{25})=2

(c)\log_2(\dfrac{64}{8})=3

(d)\log_4(\dfrac{64}{16})=1

(e)\log_6(36^4)=8

(f)\log(100^3)=6

Step-by-step explanation:

Let as consider the given equations are \log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?.

(a)

\log_3(\dfrac{81}{3})=\log_3(27)

\log_3(\dfrac{81}{3})=\log_3(3^3)

\log_3(\dfrac{81}{3})=3        [\because \log_aa^x=x]

(b)

\log_5(\dfrac{625}{25})=\log_5(25)

\log_5(\dfrac{625}{25})=\log_5(5^2)

\log_5(\dfrac{625}{25})=2        [\because \log_aa^x=x]

(c)

\log_2(\dfrac{64}{8})=\log_2(8)

\log_2(\dfrac{64}{8})=\log_2(2^3)

\log_2(\dfrac{64}{8})=3        [\because \log_aa^x=x]

(d)

\log_4(\dfrac{64}{16})=\log_4(4)

\log_4(\dfrac{64}{16})=1        [\because \log_aa^x=x]

(e)

\log_6(36^4)=\log_6((6^2)^4)

\log_6(36^4)=\log_6(6^8)

\log_6(36^4)=8            [\because \log_aa^x=x]

(f)

\log(100^3)=\log((10^2)^3)

\log(100^3)=\log(10^6)

\log(100^3)=6            [\because \log10^x=x]

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Step-by-step explanation:

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Step-by-step explanation:

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So, P(B) = 0.35

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the probability that the dancer likes ballet if we know she likes tap. This is the case of conditional probability.

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6 0
3 years ago
How do you solve 3 1/4 - 1 5/6
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Answer:

to solve 3\frac{1}{4} -1\frac{5}{6}  you would first need to convert them from mixed numbers to improper fractions. You can do this by multiplying the denominator with the whole number and then adding the numerator.  Then you should make sure that the denominators are the same. You can do this by first finding a number that they will both multiply into. In this example it is 12. And when changing the denominator you must apply it to the numerator.  So if you multiplied the denominator by 3 then you must multiply the numerator by 3. After you can just minus the numerators. However remember to keep the denominator the same. Then you can change it back into a mixed number by dividing the numerator by the denominator and having that whole number on the side of the fraction . lets say it is \frac{13}{6} then you would divide 13 by 6 which is 2 and a decimal and then minus the number that is multiplied by the numerator and it will give a number that is smaller than the denominator and then it would become 2\frac{1}{6}.

Step-by-step explanation:

1) Change the fractions to improper fractions.

   \frac{13}{4} -\frac{11}{6}

2) Change the  denominator to a common denominator.

\frac{39}{12} -\frac{22}{12}

3) Minus the Numerators.

\frac{39}{12} -\frac{22}{12}=\frac{17}{12}

4) Changing it to a mixed number

=1\frac{5}{12}

6 0
3 years ago
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