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RSB [31]
2 years ago
14

8^5 = 2^2m+3 Solve m

Mathematics
1 answer:
ziro4ka [17]2 years ago
8 0

Answer:

m=6

Step-by-step explanation:

<u>Exponent properties</u>:

We can use exponent property a^{b^c}=a^{(b\cdot c)} to solve this problem.

Rewrite 8 as 2^3, then apply exponent property a^{b^c}=a^{(b\cdot c)} to simplify:

2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}

If a^b=a^c, then b=c, because of log property \log a^b=b\log a. Using this log property, you can take the log of both sides and divide by \log a to get b=c

Therefore, we have:

15=2m+3

Subtract 3 from both sides:

12=2m

Divide both sides by 6:

m=\frac{12}{2}=\boxed{6}

<u />

<u>Alternative</u>:

Given 8^5=2^{2m+3}, to move the exponent down, we'll use log properties.

Start by simplifying:

\log 32,768=2^{2m+3}

Take the log of both sides, then use log property \log a^b=b\log a to move the exponent down:

\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2

Divide both sides by \log2:

2m+3=\frac{\log (32,768)}{\log(2)}

Subtract 3 from both sides:

2m=\frac{\log (32,768)}{\log(2)}-3

Divide both sides by 2:

m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}

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Kristen can type a 50-page paper in 8 hours. Last month, Kristen and Courtney typed a 50-page paper in 6 hours. How long would i
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24 hours

Step-by-step explanation:

Kristen = 8 hours

Kristen and Courtney = 6 hours

Courtney = x hours

in six hours kirsten can do 6/8 of the job

6/8 = 3/4

So kirsten is going to be doing 3/4 of the job

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5 0
2 years ago
What is the product of 4 and 8V200 in simplest radical form?
Sonja [21]

Answer:

320√2

Step-by-step explanation:

4 * 8√200

= 4 * 8√2√100

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4 0
2 years ago
What do you notice about the ratios of the lengths for each transversal? How do they compare?
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3 years ago
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to make a shade of plant called Jasper Green, Mix 4 quarts of green paint with 2/3 cups of black paint. how much green paint sho
r-ruslan [8.4K]

Answer

24 quarts of green paint should be mixed with 4 cups of black paint.

That is (96 cups)

Step by step explanation

Jasper Green mix 4 quarts of green paint with 2/3 cups of black paint.

Let's convert 4 quarts into cups.

1 quart = 4 cups

4 quarts = 16 cups

Here mix 16 cups of green paint with 2/3 cups of black paint.

Let's use the proportion

Green paint                      Black paint

16                                          2/3

x                                            4

16/x =2/3 divided by 4

\frac{16}{x}  = \frac{2/3}{4}

Cross multiplying, we get

16*4 = 2/3 x

64 = 2/3 x

x = 64/(2/3)

x = 64 * 3/2

x = 192/2

x = 96 cups

96 cups of green paint should be mixed with 4 cups of black paint.

We can covert 96 cups into quarts by dividing by 4

96/4 = 24 quarts

24 quarts of green paint should be mixed with 4 cups of black paint.

Thank you.

4 0
3 years ago
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