SOLUTION: Use log4(7) ≈ 1.4037 and log4 (3) ≈ 0.7925 to approximate the value of each expression. log4 (21) and log4 (7/12) Thanks.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Use log4(7) ≈ 1.4037 and log4 (3) ≈ 0.7925 to approximate the value of each expression. log4 (21) and log4 (7/12) Thanks.       Log On


   

Question 1039802: Use log4(7) ≈ 1.4037 and log4 (3) ≈ 0.7925 to approximate the value of each expression.
log4 (21)
and
log4 (7/12)
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the log rules to say

log%284%2C%2821%29%29=log%284%2C%283%2A7%29%29
log%284%2C%2821%29%29=log%284%2C%283%29%29%2Blog%284%2C%287%29%29
log%284%2C%2821%29%29=0.7925%2B1.4037
log%284%2C%2821%29%29=2.1962 (this is approximate)

and

log%284%2C%287%2F12%29%29=log%284%2C%287%2F%283%2A4%29%29%29
log%284%2C%287%2F12%29%29=log%284%2C%287%29%29-log%284%2C%283%2A4%29%29
log%284%2C%287%2F12%29%29=1.4037-%28log%284%2C%283%29%29%2Blog%284%2C%284%29%29%29
log%284%2C%287%2F12%29%29=1.4037-%280.7925%2B1%29
log%284%2C%287%2F12%29%29=1.4037-1.7925
log%284%2C%287%2F12%29%29=-0.3888 (this is also approximate)