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log10 4th root of (y^3/20x^5)
_________
/ y3
log10\ 4/ -------
\/ 20x5
Write the 4th root as the 1/4th power
_
|¯ y3 |1/4
log10|------|
|_20x5 |
¯
Use the rule logbac = c·logba
_
|¯ y3 |
1/4·log10|------|
|_20x5 |
Use the rule logb(a/c) = logba - logbc
1/4[log10y3 - log10(20x5)]
Use the rule logb(ac) = logba + logbc
1/4[log10y3 - (log1020 + log10x5)]
Remove the parentheses
1/4[log10y3 - log1020 - log10x5]
Use the rule logbac = c·logba on 1st and 3rd terms:
1/4[3·log10y - log1020 - 5·log10x]
Write the 20 as (2·10)
1/4[3·log10y - log10(2·10) - 5·log10x]
Use the rule logb(ac) = logba + logbc on middle term
1/4[3·log10y - (log102 + log1010) - 5·log10x]
Remove the parentheses:
1/4[3·log10y - log102 - log1010 - 5·log10x]
Use the rule logbb = 1 on third term:
1/4[3·log10y - log102 - 1 - 5·log10x]
Edwin
