SOLUTION: Please Help! Use properties of logarithms or a definition to simplify the expression. Log base 6 (1/6) and please explain answer step by step. Thanks!

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Question 737043: Please Help!
Use properties of logarithms or a definition to simplify the expression.
Log base 6 (1/6)
and please explain answer step by step. Thanks!
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We are using these 3 rules (in the same order)

Rule 1) 1/x = x^(-1)

Rule 2) log(x^y) = y*log(x)

Rule 3) log base b (b) = 1 ... ex: log%282%2C%282%29%29=1, log%2817%2C%2817%29%29=1

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Log base 6 (1/6) = Log base 6 (6^(-1)) ... use rule 1 above

Log base 6 (1/6) = -1*Log base 6 (6) ... use rule 2 above

Log base 6 (1/6) = -1*1 ... use rule 3 above

Log base 6 (1/6) = -1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%286+%2C%281%2F6%29+%29..in base 10 will be

log%2810+%2C%281%2F6%29+%29%2Flog%2810%2C6%29

log%2810+%2C%281%2F6%29+%29=-0.77815125038364363250876679797960833596831874565280
log%2810%2C6%29=0.7781512503836436325087667979796083359683187456528044

log%2810+%2C%281%2F6%29+%29%2Flog%2810%2C6%29=-0.778%2F0.778=-1