Question: Power of 5

Comment on Power of 5

how did you know that we should rise both sides with 1/3. I mean how can we find connection between the power the should we use and numbers in the questions. is there any clue we have to follow?
greenlight-admin's picture

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

greenlight-admin's picture

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 without watching the solution.

Would it also be correct to take 5^3x and simplify it to (5^x)^3 and then simplify both sides by taking the cube root of both sides to get cube root 4=5^x? Then I would know that 5^-x=1/cube root 4?
greenlight-admin's picture

That's a perfectly valid approach.
Nice work!

Hi Brent, to clarify if (5^x)^3 = 4^3, with the same exponenet so 5^x = 4 ?
Find it hard to see how 5^x = 4^3 ? Could you clarify? Thanks
greenlight-admin's picture

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, can you help me to solve the below in quick and easy way

QA QB
√160 + √40 √110 + √90
greenlight-admin's picture

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

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