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Comment on Power of 5
how did you know that we
Our goal is to find the value
Our goal is to find the value of 5^-x
Once we know that 5^3x = 4, we should ask ourselves "What must I do to 5^3x to get 5^x?"
At that point, we should focus on the exponent, and see that we can get x by multiplying 3x by 1/3
This means we should raise 5^3x to the power of 1/3
Our goal is to find the value
Our goal is to find the value of 5^-x
Once we know that 5^3x = 4, we should ask ourselves "What must I do to 5^3x to get 5^x?"
At that point, we should focus on the exponent, and see that we can get x by multiplying 3x by 1/3
This means we should raise 5^3x to the power of 1/3
Understood now. I got stuck
Would it also be correct to
That's a perfectly valid
That's a perfectly valid approach.
Nice work!
Hi Brent, to clarify if (5^x)
Find it hard to see how 5^x = 4^3 ? Could you clarify? Thanks
Yes, if (5^x)^3 = 4^3, then
Yes, if (5^x)^3 = 4^3, then we can conclude that 5^x = 4
To better understand how 5^x can equal 4, notice that 5^0 = 1 and 5^1 = 4.
So, if 5^x = 4, then x must have a value between 0 and 1.
Hi Brent, I have a question,
QA QB
√160 + √40 √110 + √90
I believe the fastest
I believe the fastest approach would be to use the on-screen calculator to evaluate each quantity.
Alternatively, here's a solution that doesn't rely on the calculator:
QUANTITY A: √160 + √40
QUANTITY B: √110 + √90
Simplify the three roots that can be simplified:
QUANTITY A: 4√10 + 2√10
QUANTITY B: √110 + 3√10
Subtract 3√10 from both quantities:
QUANTITY A: 3√10
QUANTITY B: √110
Rewrite Quantity A as follows:
QUANTITY A: (√9)(√10)
QUANTITY B: √110
Rewrite Quantity A as follows:
QUANTITY A: √90
QUANTITY B: √110
At this point, we can see that quantity B is greater.
Answer: B