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3 years ago

10

How should the decimal point in 34.05 be moved to determine the product 34.05×106 ?

1 answer:

r-ruslan [8.4K]3 years ago

3 0

Answer: Six places to the right

Step-by-step explanation:

For this exercise it is important to remember that. by definition, the exponent of a number indicates the number of times you must use the same factor to multiply.

Given:

$b^n$

"b" is the base and "n" is the exponent.

In this case, you have the following multiplication provided in the exercise:

$34.05*10^6$

Notice that the base 10 has an exponent 6. This indicates the following:

$10^6=10*10*10*10*10*10=1,000,000$

By definition, moving the decimal point 6 places to the right (because there are six zeros), is the same as multiplying the decimal number 34.05 by 1,000,000.

Therefore, based on the explained, when you move the decimal point six places to the right, you get the following product.

$34.05*10^6=34,050,000$

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Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)

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Considering the given equation $y = log_{3}x\\$

And the ordered pairs in the format $(x, y)$

I don't know if it is log of base 3 or 10, but I will assume it is 3.

For $(\frac{1}{3}, a_{0} )$

$x=\frac{1}{3}$

$y=a_{0}$

$y = log_{3}x\\y = log_{3}(\frac{1}{3} )\\y=-\log _3\left(3\right)\\y=-1$

So the ordered pair will be $(\frac{1}{3}, -1 )$

For $(1, a_{1} )$

$x=1$

$y=a_{1}$

$y = log_{3}x\\y = log_{3}1\\y = log_{3}(1)\\Note: \log _a(1)=0\\y = 0$

So the ordered pair will be $(1, 0 )$

For $(3, a_{2} )$

$x=3$

$y=a_{2}$

$y = log_{3}x\\y = log_{3}3\\y = 1$

So the ordered pair will be $(3, 1 )$

For $(9, a_{3} )$

$x=9$

$y=a_{3}$

$y = log_{3}x\\y = log_{3}9\\y=2\log _3\left(3\right)\\y=2$

So the ordered pair will be $(9, 2 )$

For $(27, a_{4} )$

$x=27$

$y=a_{4}$

$y = log_{3}x\\y = log_{3}27\\y=3\log _3\left(3\right)\\y=3$

So the ordered pair will be $(27, 3 )$

For $(81, a_{5} )$

$x=81$

$y=a_{5}$

$y = log_{3}x\\y = log_{3}81\\y=4\log _3\left(3\right)\\y=4$

So the ordered pair will be $(81, 4 )$

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4 years ago