SOLUTION: Let a= log x, b = log y and c = log z Write log (x^2 root y/z^3) in terms of a, b and c Thanks

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Question 236461: Let a= log x, b = log y and c = log z
Write log (x^2 root y/z^3) in terms of a, b and c
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28%28x%5E2%2Asqrt%28y%29%29%2Fz%5E3%29%29 Start with the given expression.


log%28%28x%5E2%2Asqrt%28y%29%29%29-log%28%28z%5E3%29%29 Break up the log using the identity log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29


log%28%28x%5E2%29%29%2Blog%28%28sqrt%28y%29%29%29-log%28%28z%5E3%29%29 Break up the first log using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29


log%28%28x%5E2%29%29%2Blog%28%28y%5E%281%2F2%29%29%29-log%28%28z%5E3%29%29 Convert to rational exponent notation.


2log%28%28x%29%29%2B%281%2F2%29log%28%28y%29%29-3log%28%28z%29%29 Pull down the exponents using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


2a%2B%281%2F2%29b-3c Now use the equations a=log%28%28x%29%29, b=log%28%28y%29%29, and c=log%28%28z%29%29


So log%28%28%28x%5E2%2Asqrt%28y%29%29%2Fz%5E3%29%29=2a%2B%281%2F2%29b-3c where a=log%28%28x%29%29, b=log%28%28y%29%29, and c=log%28%28z%29%29