Express the followings as a single logarithm: (a) 3log a x + 2log a y - 1/4log a z?

Express the followings as a single logarithm:


(a) 3log a x + 2log a y - 1/4log a z





(b) 1/3log a w - 3log a x - 5log a y





(c) 7(4log a m + 1/3log a n)

Express the followings as a single logarithm: (a) 3log a x + 2log a y - 1/4log a z?
(a) 3log a x + 2log a y - 1/4log a z


=log_a (x^3) + log_a (y^2) - log_a (z^[1/4}


= log_a ( x^3 y^2 /z^{1/4} )





(b) 1/3log a w - 3log a x - 5log a y


= log_a (w^{1/3}) - log_a (x^3) - log_a (y^5)


= log_a ( w^{1/3} /x^3 y^5)





(c) 7(4log a m + 1/3log a n) = log_a (m^28 n^ 7/3)
Reply:(a) 3log a x + 2log a y - 1/4 log a z





the numbers in front of log become exponents so:





log a x^3 + log a y^2 - log a z^(1/4)





adding logs is multiplying the insides so:





log a (x^3)(y^2) - log a z^(1/4)





subtracting logs is like dividing so:





log a [(x^3)(y^2)]/(z^(1/4))





(b) 1/3log a w - 3log a x - 5log a y





log a w^(1/3) - log a x^3 - log a y^5





log a (w^(1/3))/(x^3) - log a y^5





log a [(w^(1/3))/(x^3)]/(y^5)





(c) 7(4log a m + 1/3log a n)





Parentheses first (whatever inside you do first):





7(log a m^4+ log a n^(1/3))





7(log a (m^4)(n^(1/3))





7log a (m^4)(n^(1/3)) or log a [(m^4)(n^(1/3))]^7

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