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saul85 [17]
3 years ago
9

How to solve 12^r=13 in solving exponential equation with logarithms

Mathematics
2 answers:
oksian1 [2.3K]3 years ago
8 0
12^r=13\\
r=\log_{12}13
laila [671]3 years ago
4 0
12^r = 13

Take the logarithm of each side of the equation:

r log(12) = log(13)

Divide each side by log(12) :

r = log(13) / log(12) = 1.03221,,, (rounded)
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X=7 and x+1=8 are two consecutive integers.

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Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long.
givi [52]
<h2>Hello!</h2>

The answer is: There are a total of 16 skits in the video.

<h2>Why?</h2>

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

TotalDuration=Introduction+n*Skit

Second equation:

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Where,

TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes

So, replacing and substituting the second equation into the first equation we have:

101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes

Have a nice day!

8 0
3 years ago
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2y to the power of 4 x 5y to the power of 3
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Answer:

(2•5y to the 7th power)

Step-by-step explanation:

Step 1:  (2y to the 4th power • 5) • y to the 3rd power

Step 2:  (2•5y to the 4th power) • y to the 3rd power

Step 3:  3.1    y to the 4th power multiplied by y to the 3rd power = y to the  (4 + 3) power = y to the 7th power

Final answer:  (2•5y to the 7th power)

6 0
3 years ago
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