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sergeinik [125]
3 years ago
6

Please help! The answer to this is 2 but I don't know how to actually solve it so can someone please show the work for this?

Mathematics
2 answers:
s344n2d4d5 [400]3 years ago
4 0

Answer:

2

Step-by-step explanation:

basically logarithms are like reverse exponents

log7, 49 is basically asking 7 to the what gets you 49

because of that its 2 because 7^2 gets you 49

svetoff [14.1K]3 years ago
3 0
<h3>Answer:    2</h3>

========================================================

Explanation:

Recall that any exponential equation of the form b^x = y can be written into its equivalent log form of \log_{b}(y) = x. Note how in both cases, 'b' is the base. For the exponential equation, x is buried in the exponent and y is free on its own. In the log equation, we have y buried in the log and x is free or isolated on its own.

In your case, we have b = 7 and y = 49. This means \log_{7}(49) = x is the same as 7^x = 49 when converting from log form to exponential form. Then we can rewrite that 49 into 7^2 to get 7^x = 7^2. The bases are both 7, so the exponents must be the same as well. Therefore, x = 2.

-------------------

We could follow a different approach. We could apply the change of base formula. The change of base formula is

\log_{b}(x) = \frac{\log(x)}{\log(b)}

On the left side, we have log base b; however, on the right side, the log can be any base we want. Oftentimes it's handy to go with base 10, though again it doesn't matter the base on the right hand side logs.

So we would then say...

\log_{b}(x) = \frac{\log(x)}{\log(b)}\\\\\log_{7}(49) = \frac{\log(49)}{\log(7)}\\\\\log_{7}(49) = \frac{1.69019608002851}{0.84509804001426}\\\\\log_{7}(49) = 1.99999999999999\\\\

Due to rounding error, we don't land exactly on 2 as expected. However, we get close enough.

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STatiana [176]
480 pennies.

25% are dated before 1980, therefore:
1200(total):100 = 12 (1%)
12(1%)x25 = 300 (25%)

35% are dated from 1980 to 2000, therefore:
12(1%)x35 = 420 (35%)

25% are dated before 1980, 35% are dated from 1980 to 2000 and the rest are dated after 2000.
25% + 35% = 60%.
300(25%) + 420(35%) = 720.
60% = 720.
100%-60% = 40%.
40% is the amount of pennies that are dated after 2000.

The total (100%) of the pennies is 1200.
We also know that 60% of the total (1200) is 720.

1200(100%) - 720(60%) = 480(40%).

Therefore, the amount of pennies dated after 2000 in Russell’s Collection is 480.
7 0
3 years ago
there are 24 marbles in a bag: 2/16 of the marbles are red, 1/8 of the marbles are blue, 1/4 of the marbles are yellow, 1/3 of t
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Step-by-step explanation:

I know these are the correct number of marbles because I set up these numbers as fractions and solved for x.

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You would do this because we are trying to find the number of marbles that are red out of the 24 marbles.

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4 0
2 years ago
Absolute Bagels makes bagels using two different recipes, one recipe for regular bagels
shutvik [7]

Answer:

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Step-by-step explanation:

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8 0
2 years ago
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Answer:

I think the answer to the question should be C

Step-by-step explanation:

3 0
3 years ago
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Alex

I can't see the picture, can you please explain the problem in the comment bar below this so can edit my answer to help?

7 0
3 years ago
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