Harvard University Interview Tricks.

Thanks

Wow❤

You lenghten solution steps… it is not satisfactory

Great breakdown, thank you.

I don't know what constitutes a properly reduced answer. I took a different approach towards the end. My strategy was to make the integer component as large as possible.
1. 4^(x-2)=40
2. 4^x/4^2=40
3. 4^x=16(40)
4. x=logb4(640) # logb4 = base 4 as I don't know how to get my subscript on 😀

# Pull out the easy powers of 4
5. x=logb4(16*4*10)

6. x=logb4(16)+logb4(4)+logb4(10)

7. # Reduce the easy parts to integers
x=2+1+logb4(10)

8. # Simplify
x=3+logb4(10)

9. # Here's where we differ. I do not like that the 10 is greater than the base 4, since that means I have another integer in there somewhere.
# So I factor that 4 out. Remember, if brute force does not work, you aren't using enough of it!
x = 3 + logb4(4 * 2.5)
x= 3 + logb4(4)+logb4(2.5)

10. Now I want my integer!
x= 3 + 1 + logb4(5/2)
x = 4 + logb4(5/2)

11. Let's address that fraction
x = 4 + logb4(5) - logb4(2)

And I'd probably stop there as there are no fractions anywhere. I don't have a logical reason right now why I am not pulling an integer out of logb4(5) (I'll go try it to see what happens) but I suspect it's not going to increase clarity if I do.

You took the long way around - here is what I did
4^(x-2) = 40
divid by 4

4^(x-3) = 10
take log


(x-3) log (4) = log (10 )
log 10 == 1

(x-3) log (4) = 1
divid by log(4)

x-3 = 1/log(4)
add 3

x = 3 + 1/log(4)
calculator

x = 4.66096
-------------------------

his answer
x = 3.5 + log2(5)/2
that log is 2.321928
divid by 2 and add 3.5 = 4.66096

X=4.66905

Your solution steps are too long.
4^(x-2) = 4^1 × 10
(x-2)log4 = log4 + log10
x-2 = 1 + 1/log4
x = 3 + 1/log4 = 4.661

💯✔️👍🇮🇳

There is a faster way. Divide both sides by 4 to get 4^(x - 3) = 10. Then, since 4 = 2^2, you can write it (2^2)^(x-3) = 10 or 2^(2x - 6) =10. Divide both sides by 2 to get 2^(2x - 7) = 5. Then take the log on both sides to get (2x - 7) log(2) = log(5) which gives 2x - 7 = log(5) / log(2) then 2x = 7 + log(5) / log(2) and finally x = 3.5 + log(5) / log(2). I leave it like that since most calculators can calculate the log in base 10 and base e but not base 2.

4,...?

🥲

x=log_4(640)

You are stupid or idiot

your way is very easy to understand!

Hello 4^x/4^2=40 === 640/16=40 end

Thank you

4 ^ (x - 2) = 40
x - 2 = log(base4)(40)
x = 2 + log(base4)(40)
x = 2 + log(40) / log(4) = 4,661

Я методом подбора решила, что х равен минус 2.

Very sloppy notation; the equals sign should be at the same level as the fraction bar.

Here’s a shortcut:
1. 4^(x-2)=40
2.x-2log4=log40
3.x-2=log4(40)
4.x=log4(40)+2