Asked by dam

if loxbase 2=k^2+2k
what is the value of logx^3 base64
Answered by Reiny
log<sub>2</sub> x = k^2+2k
then x = 2^(k^2 + 2k)

let
log<sub>64</sub> x^3 = y
then 3 log<sub>64</sub> x = y
log<sub>64</sub> 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

log<sub>64</sub> 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<sub>a</sub> x ) รท log<sub>(a^n)</sub> x
= n

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