Exponent Problem: Given 5^21 * 4^11 = 2 * 10^n, find n

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mcheytan

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Given the equation: 5^21 x 4^11=2 x 10^n
what is "n"???

I simplified the equation to get
10^n=5^21 x 2^11

I am not sure how to find n...is there anything I can do seeing that i have 5 on a power and 2 on a power, which if multiplied on 1st power equal 10....
 
Re: Exponent Problem

Take the log:

\(\displaystyle log(\frac{5^{21}\cdot{4^{11}}}{2})=21log(5)+22log(2)-log(2)=21(log(5)+log(2))=21log(10)=21\)
 
Re: Exponent Problem

Another approach.

2 x 10^n = 5^21 x 4^11 = 5^21 x 2^22 = 5^21 x 2^21 x 2 = 2 x (5 x 2)^21 = 2 x 10^21.

n=21
 
Re: Exponent Problem

Why is there an addition between 21log(5) and 21log(2)...shouldn't it be multiplication since the original equation has multiplication? It would also make sense because we take 21log in front of parentheses in which we have 5x2 and thats how we get 10???
 
Re: Exponent Problem

Properties of logs. \(\displaystyle log(a*b)=log(a)+log(b) \;\ and \;\ log(a/b)=log(a)-log(b)\)
 
So once I have 21log(5) + 21log(2) how to I get that it equals= 21log10?? when I have addition of 2 and 5 not multiplication?
 
mcheytan said:
Given the equation: 5^21 x 4^11=2 x 10^n
what is "n"???
I simplified the equation to get
10^n=5^21 x 2^11
Click to expand...
That is not correct; should be 10^n = (5^21 * 4^11) / 2
So you're sure not ready for this type of problem; better talk to your teacher.

You seem to think that 4^2 / 2 = 2^2 ; it is NOT.
4^2 / 2 = 16 / 2 = 8
2^2 = 4
 
Yesssss that really was wrong and I know why, I just did not go through the correct process when changing from 4^11 to 2^xx, that is why I did not have it right. I understand now.
Thanks
 
mcheytan said:
So once I have 21log(5) + 21log(2) how to I get that it equals= 21log10?? when I have addition of 2 and 5 not multiplication?
Click to expand...
That is the final question I have :p
 
mcheytan said:
mcheytan said:
So once I have 21log(5) + 21log(2) how to I get that it equals= 21log10?? when I have addition of 2 and 5 not multiplication?
Click to expand...
That is the final question I have :p
Click to expand...

use pencil & paper.

factor out 21 - what do you have left?

apply rule of logarithm.
 
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