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sergeinik [125]
2 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]2 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]2 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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In a school of 330 students, 85 of them are in a drama club, 200 of them are in a sports team and 60 of them do both
Neko [114]

Answer:

105/330 = 21/66 = 7/22

7/22 is the answer I think

Step-by-step explanation:

n(U) = 330

n(A) = 85

n(B) = 200

n(A n B) = 60

Now,

n(A U B) = n(A) + n(B) - n(A n B)

or, n(A U B) = 85 + 200 - 60

or, n(A U B) = 285 - 60 = 225

Now,

n(A U B) compliment = n(U) - n(A U B)

n(A U B) compliment = 330 - 225

so, n(A U B) compliment = 105

Now,

probability = 105/330

8 0
2 years ago
Answer for 14+3y &lt; 65
ivanzaharov [21]
Hey there!

14 + 3y < 65

SOME people replace “<”, “>”, “≥”, or “≤” as an equal sign (=) to make it easier to solve

14 + 3y < 65
14 + 3y = 65

SUBTRACT by 14 on both of your sides
3y + 14 - 14 = 65 - 14
CANCEL out: 14 - 14 because that gives you 0
KEEP: 65 - 14 because it helps you solve for “y”

**65 - 14 = 51**

NEW EQUATION: 3y = 51

DIVIDE by 3 both of your sides
3y/3 = 51/3
CANCEL out: 3/3 because that gives you 1
KEEP: 51/3 because it gives you the value of “y”



NEW EQUATION: y = 51/3

**51/3 = 17**

Answer: y = 17 ☑️

☑️ OVERALL ANSWER FOR YOU: y < 17 ☑️
NOTE: it’s an OPEN circle SHADED to the LEFT

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

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Step-by-step explanation:

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