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Question: If 5^x – 5^(x- 3) = 124*5^y, what is y in terms of x?
Pre- analysis
1. Notice that 124 is 1 less than 125, i.e - 5^3
2. On the LHS you have 5^x – 5^(x- 3)
Working from the LHS
5^3 gives us 125, we need to subtract this by 1 to get 124
hence, we would need 5^(x- 3) to equal 1. This can only happen if 5^0 and x = 3
Hence, our LHS becomes: 5^3 - 5^(3-3)
Same thing on the RHS
We need to keep 124, and this can be done by multiplying it with 1. This can only happen if 5^0
Finally we have: 5^3 - 5^(3-3) = 124 * 5^0
5^3 - 5^0 = 124 * 5^0
125-1 = 124*1
124=124
Hence: x=3, y=0
and y= x-3
I hope this helps those weak in quants (like myself)!
Pre- analysis
1. Notice that 124 is 1 less than 125, i.e - 5^3
2. On the LHS you have 5^x – 5^(x- 3)
Working from the LHS
5^3 gives us 125, we need to subtract this by 1 to get 124
hence, we would need 5^(x- 3) to equal 1. This can only happen if 5^0 and x = 3
Hence, our LHS becomes: 5^3 - 5^(3-3)
Same thing on the RHS
We need to keep 124, and this can be done by multiplying it with 1. This can only happen if 5^0
Finally we have: 5^3 - 5^(3-3) = 124 * 5^0
5^3 - 5^0 = 124 * 5^0
125-1 = 124*1
124=124
Hence: x=3, y=0
and y= x-3
I hope this helps those weak in quants (like myself)!
19 Nov 2022, 14:23
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Bunuel
Bunuel
Why can't 5^x - 5^(x-3) be converted to 5^3? ---> if you subtract the exponents, x-x+3=3
Both terms have the same base of 5, so why can't the exponents simply be subtracted here? Thank you!
20 Nov 2022, 01:29
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woohoo921
You'd be right if we had division instead of subtraction:
\(\frac{5^x}{5^{x-3}}=5^{x-(x-3)}=5^{3}\).
I think you might benefit from going through basics again.
8. Exponents and Roots of Numbers
