Which logs between 4 and 9 (including 4 and 9) can be found from the logs of 2 or 3? List the logs and show work!! like the
example.
ex. log4(2*2)?
use the following log rules.
log(a^b) = b log(a) ---------------rule (1)
log(a/b) = log(a) - log(b) --------rule(2)
log(ab) = log(a) + log(b) --------rule (3)
log(4) = log(2^2) = 2 log(2) -------------------------- ( rule 1)
log(5) = log(10/2) = log(10) - log(2)= 1 - log(2) ------(rule 2)
log(6) = log(2*3) = log(2) + log(3) ------------------------(rule 3)
log(8) = log(2^3) = 3 log(2) ---------------------------------rule(1)
log(9) = log(3^2) = 2 log(3) ---------------------------------rule(1)
log(4) = log(2*2) = 2log(2)
log(5) = log(10/2) = log(10) - log(2) = 1 - log(2)
log(6) = log(2*3) = log(2) + log(3)
log(8) = log(2^3) = 3 log(2)
log(9) = log(3^2) = 2 log(3)
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Verified answer
use the following log rules.
log(a^b) = b log(a) ---------------rule (1)
log(a/b) = log(a) - log(b) --------rule(2)
log(ab) = log(a) + log(b) --------rule (3)
log(4) = log(2^2) = 2 log(2) -------------------------- ( rule 1)
log(5) = log(10/2) = log(10) - log(2)= 1 - log(2) ------(rule 2)
log(6) = log(2*3) = log(2) + log(3) ------------------------(rule 3)
log(8) = log(2^3) = 3 log(2) ---------------------------------rule(1)
log(9) = log(3^2) = 2 log(3) ---------------------------------rule(1)
log(4) = log(2*2) = 2log(2)
log(5) = log(10/2) = log(10) - log(2) = 1 - log(2)
log(6) = log(2*3) = log(2) + log(3)
log(8) = log(2^3) = 3 log(2)
log(9) = log(3^2) = 2 log(3)