Can anyone solve these Logorithmic Equations (grade 12 academic level)?????

Question

If log2(log3a)=2, determine the value of a. (Answer:81)

Note: The 2 after the first log is a subscript as well as the 3a after the second log.

If log2n(1994) = logn(486sqr2), determine the value of n^6.
(Answer: 2.23 8 10^11)

Note: The 2n after the first log is a subscribt and the n after the second log is also a subscribt. Also note that the 2 is squarerooted.

Please show all the steps. It would really help!!

No, theres no typo. I've checked. Its a hard question.

Answer 1

For the first one, start by taking 2 to the power of each sides. The answers of course are equal. On one side you just get 2^4 = 4. On the other, by the definition of log, you get log-base-3-of-a.

Apply the same idea again, and you get a = 3^4 = 81.

For the second one, start by taking 2n to the power of each side. On the RHS, 2n to the power of any k is of course 2^k * n*k.

I won't work out the exact numbers because, among other things, I'm having trouble believing that there's no typo in the answer you gave.