Find the rational values of $k$ for which $$\sqrt[3]{\log_3(k)}=2^\frac23$$ I have tried to write it as $$\left(\log_3k\right)^\frac13=2^\frac23$$ but I don't know if this is helpful or not. Thank you!
Asked
Active
Viewed 58 times
1
-
2How about starting by raising woth sides to the power of $3$? What do you get? – Gary Jan 01 '22 at 23:50
-
3@Gary, thank you! We get $$\log_3(k)=4\iff k=3^4=81.$$ – mat1 Jan 01 '22 at 23:58
-
You are right. ${}$ – Gary Jan 01 '22 at 23:59
1 Answers
0
Hint: $2^{\frac{2}{3}} = \sqrt[3]{2^2}= \sqrt[3]{4}\implies \sqrt[3]{\log_3 k} = \sqrt[3]{4}$. Can you take it from here?
Wang YeFei
- 6,390