6=3 square - 3 power 1

10b) and 11 are typical A Math questions from first impression.

There might have have been some typo or mis-pasting of questions by the setter/teacher.


If 10b) were to be solved using E Math methods only then there's only 1 possible answer (no using of logarithms)

And it's by observation. (actually guess and check)


I will use superscript n in place of x.
(superscript x not available on my keyboard)


3²ⁿ+¹ + 6 = 3ⁿ+²

(3²ⁿ)(3¹) + 6 = (3ⁿ)(3²)

3(3ⁿ)² + 6 = 9(3ⁿ)

(3ⁿ)² + 2 = 3(3ⁿ)

By observation,

(3°)² + 2
= 1² + 2
= 1 + 2
= 3
= 3 x 1
= 3(3°)

So n = 0


Or,


6
= 9 - 3
= 3² - 3¹
= 3°+² - 3²(°)+¹

By oberservation, n = 0


Or


(3ⁿ)² + 2 = 3(3ⁿ)
2 = 3(3ⁿ) - (3ⁿ)²


But 2 = 3 - 1
= 3 x 1 - 1²
= 3(3°) - (3°)²

By observation, n = 0

I got 2 answers too. 3^x=1 and 3^x=2 . One answer is 0. Another one I guess by comparing the values of 3^0.5 and 3^0.7 in the calculator. The value of 3^0.7 is more than 2, so the power is less than 0.7. In other words, the value of the power is within 0.63 to 0.64. If without using logarithms, the best value I can get is 0.6309 lol... as the value is 1.999934626 which is closest to 2. Can try using graph lol but is quite tedious since log isn't covered in e math. Or put 3^x=2 as rejected like how we rej two answers in a quadratic equation lol. I don't think there is a way to solve using laws of indices because 3^x=3^0*2=2. We have to figure out what 3^n is to get 2 in order to find x. I would just use guessing method.

Iterative method would take ages... This is most likely a mis-copying and pasting of the questions by the teacher/setter.

Hey guys! Thank you for taking the time to try to attempt the E Math way. I think we all agree that it's a mistake on the teacher's end because as said, observation method is not ideal yet it is the only way to work around this. Nonetheless I really appreciate taking the time to work this out with me!!

Welcome