Question

if loxbase 2=k^2+2k

what is the value of logx^3 base64

Answer 1

log₂ x = k^2+2k

then x = 2^(k^2 + 2k)

let
log₆₄ x^3 = y
then 3 log₆₄ x = y
log₆₄ x = y/3

64^(y/3) = x
then:
64^y = x^3 = 2^(3k^2 + 6k)
2^(6y) = 2^(3k^2 + 6k)

6y = 3k^2 + 6k
y = (1/2)k^2 + k

log₆₄ x^3 = (1/2)k^2 + k or (k^2 + 2k)/2

a quicker way might be to use a little-known rule of logs

( log_a x ) ÷ log_(a^n) x
= n