Question

Rewrite log6 /(a/b)4 . c/
using the properties of logarithms

Answer 1

Assuming the expression is log base 6 of ( (a/b)^4 · c ), i.e. log_6((a/b)^4 c), use the log rules:

1. Product rule: log_6(XY) = log_6 X + log_6 Y
2. Power rule: log_6(X^k) = k log_6 X
3. Quotient rule: log_6(X/Y) = log_6 X − log_6 Y

So
log_6((a/b)^4 c) = log_6((a/b)^4) + log_6 c
= 4·log_6(a/b) + log_6 c
= 4[log_6 a − log_6 b] + log_6 c
= 4 log_6 a − 4 log_6 b + log_6 c.