Question

Solve these inequalities.
(ii) 3^x +5 bigger or equal to 32
Please help! I don't know how to solve this though I a aware it involves logarithms. Please show me what to do and explain why.

Answer 1

\[\huge\rm 3^x +5 \ge 32\]
yes right you have to take log both sides
but first move `5` to the right side and then take log

Answer 2

make sense ?

Answer 3

So It would be \[3^{x} \ge 17\] ? How do I take log of both sides?

Answer 4

17 ?? i guess thats a typo

Answer 5

Um no actually. What did I do wrong?

Answer 6

how did you get 17 ?

Answer 7

I subtracted 5 from both sides?

Answer 8

yes right so 32-5 isn't equal to 17 :=)

Answer 9

Ooooh. I do mistakes like that often. Oops!

Answer 10

ok so after \[3^{x} \ge 27\] how do I take log of both sides?

Answer 11

yes right now take log both sides and apply the product rule \[\huge\rm log (3)^x \ge \log(27)\]

Answer 12

power rule ***

Answer 13

Ok I am new too logarithms so sorry for taking so much time. If you use the power rule does that mean that I move the exponent x in front of the first logarithm?

Answer 14

yes right :=)
and its okay take ur time!

Answer 15

Thanks! All right so,
\[x \log_{}3 \ge \log27\]

Answer 16

yes right now to solve for x you should move log(3) to the right side :=)
and then use calculator :P that's it!

Answer 17

Ok, thank you so much! :D

Answer 18

what did you get ?? o.O

Answer 19

x\[x \ge 3\]

Answer 20

yes right!

Answer 21

good job!

Answer 22

Hooray!