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brilliants [131]
3 years ago
14

Change from base 10 to the give base

Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0

Writing numbers in base 10 means to write them as a combination of powers of 10, for example

1925 = 1\cdot 10^3 + 9\cdot 10^2 + 2\cdot 10^1+5\cdot 10^0

So, writing numbers in any base means to do the same thing: for example, in base 3, we have

102_3 = 1\cdot 3^2 +0\cdot 3^1 +2\cdot 3^0 = 12_{10}

So, in order to write 80 in base 3, we have to find out the largest power of 3 that fits: we have

3^0=3,\ \ 3^1=3,\ \ 3^2=9,\ \ 3^3=27,\ \ 3^4=81

So, since 3^4 is too much, our number will have 4 digits:

abcd_3 = a\cdot 3^3 +b\cdot 3^2 +c\cdot 3^1 + d\cdot 3^0

In order to find the digits, again we see "how much it fits": we have

0\cdot 3^3 = 0\ \ 1\cdot 3^3 = 27,\ \ 2\cdot 3^3 = 54

So, we choose a=2. The remainder is 80-54=26

Now we need to fix the coefficient for 3^2: we have

0\cdot 3^2 = 0\ \ 1\cdot 3^2 = 9,\ \ 2\cdot 3^2 = 18

Again we choose b=2

Keep going like this and you'll find out that

80_3 = 2222

This was actually a special case, because our number is exactly one less than a power of 3: we have

80=3^4-1

and just like in base 10, when we subtract 1 from a power of 10 we get a number composed by 9 only:

10000000-1 = 9999999

In every base, when we subtract 1 from a power of the base we get a number composed by (base-1) only:

(10000-1)_3 = 2222

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Which exponential equation is equivalent to this logarithmic equation log x5 + log x12 =7
trapecia [35]

Answer:

x⁷ = 60

Step-by-step explanation:

<u>Given</u><u> </u><u>:</u><u>-</u><u> </u>

  • log x⁵ + log x ¹² = 7 .

<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u><u> </u>

  • The expotential equation .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

Given logarithmic equation is ,

⇒ log x⁵ + log x ¹² = 7

⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]

⇒log x ⁶⁰ = 7

In expotential form we can write it as ,

⇒ x⁷ = 60

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3 years ago
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Someone help me with this one​
frosja888 [35]

Answer:

2/3

Step-by-step explanation:

20% = 12

48

1/6 = 8

left = 40

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4/6 = 2/3

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Write the equation of the line in fully simplified slope-intercept form.
Bad White [126]

Answer:

y = -\frac{2}{5} x-6

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula m =\frac{y_2-y_1}{x_2-x_1}. Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5} \\  

So, the slope of the line is -\frac{2}{5}.

2) Next, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the m, x_1 and y_1 into the formula.

Since m represents the slope, substitute -\frac{2}{5}  in its place. Since x_1 and y_1 represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6

6 0
3 years ago
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