Answer:
![m=6](https://tex.z-dn.net/?f=m%3D6)
Step-by-step explanation:
<u>Exponent properties</u>:
We can use exponent property
to solve this problem.
Rewrite
as
, then apply exponent property
to simplify:
![2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}](https://tex.z-dn.net/?f=2%5E%7B3%5E5%7D%3D2%5E%7B2m%2B3%7D%2C%5C%5C2%5E%7B15%7D%3D2%5E%7B2m%2B3%7D)
If
, then
, because of log property
. Using this log property, you can take the log of both sides and divide by
to get ![b=c](https://tex.z-dn.net/?f=b%3Dc)
Therefore, we have:
![15=2m+3](https://tex.z-dn.net/?f=15%3D2m%2B3)
Subtract 3 from both sides:
![12=2m](https://tex.z-dn.net/?f=12%3D2m)
Divide both sides by 6:
![m=\frac{12}{2}=\boxed{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B12%7D%7B2%7D%3D%5Cboxed%7B6%7D)
<u />
<u>Alternative</u>:
Given
, to move the exponent down, we'll use log properties.
Start by simplifying:
![\log 32,768=2^{2m+3}](https://tex.z-dn.net/?f=%5Clog%2032%2C768%3D2%5E%7B2m%2B3%7D)
Take the log of both sides, then use log property
to move the exponent down:
![\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2](https://tex.z-dn.net/?f=%5Clog%2832%2C768%29%3D%5Clog%202%5E%7B2m%2B3%7D%2C%5C%5C%5Clog%20%2832%2C768%29%3D%282m%2B3%29%5Clog%202)
Divide both sides by
:
![2m+3=\frac{\log (32,768)}{\log(2)}](https://tex.z-dn.net/?f=2m%2B3%3D%5Cfrac%7B%5Clog%20%2832%2C768%29%7D%7B%5Clog%282%29%7D)
Subtract 3 from both sides:
![2m=\frac{\log (32,768)}{\log(2)}-3](https://tex.z-dn.net/?f=2m%3D%5Cfrac%7B%5Clog%20%2832%2C768%29%7D%7B%5Clog%282%29%7D-3)
Divide both sides by 2:
![m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5Clog%20%2832%2C768%29%7D%7B2%5Clog%282%29%7D-%5Cfrac%7B3%7D%7B2%7D%3D%5Cboxed%7B6%7D)
Answer:
Yes
Step-by-step explanation:
Remember in order for the rates to be proportional it has to have a constant rate of change and it has to go through the origin if graphed
For one this has a constant rate of change which is 3 dollars per 25 messages
Now we just have to find out if it would go through the origin (0,0)
To do so we subtract 3 dollars and then 25 messages
6-3=3
50 - 25 =25
then again 25-25=0
3-3=0
concluding that (0,0) is a solution
Thus meaning that this is a proportional relationship
The same number you wrote because is already rounded. ^-^
-JZ
B
I've seen my brother with this answer and he said it was correct he passed all his grades with too
Work: Y=3/(10-x )
Solve for x
×(10-x) both sides
Y (10-x)=3
10y-xy=3
-10y both sides
-xy=-10y+3
÷-y both sides
X=(10y-3)/y
Simplify
X=10y/y-3/y
X=10-3/y
Answer: x=10-3/y
Check your work: plug in x
Y=3/(10-(10-3/y))
Simplify
Y=3/(10-10+3/y)
Y=3/(3/y)
Y=3×y/3
Y=y
The answer is correct