Question 1139211
if {{{log (2) = 0.301}}} and {{{log( 3) = 0.477}}}

 solve the following showing the steps

1.
{{{ 2log(12) - 3log(6) + 2log(24)}}}

={{{ 2log((2^2*3)) - 3log((2*3)) + 2log((2^3*3))}}}

={{{ 2(log(2^2)+log(3)) - 3(log(2)+log(3)) + 2(log(2^3)+log(3))}}}

={{{ 2(2log(2)+log(3)) - 3(log(2)+log(3)) + 2(3log(2)+log(3))}}}

={{{ 4log(2)+2log(3) - 3log(2)-3log(3) + 6log(2)+2log(3)}}}

={{{ 7log(2)+log(3) }}}.....plug in given values {{{log (2) = 0.301}}} and {{{log( 3) = 0.477}}}

={{{ 7(0.301)+0.477}}}

={{{ 2.584}}}


or, you can do it this way:

{{{ 2log(12) - 3log(6) + 2log(24)}}}

={{{ log(12^2) - log(6^3) + log(24^2)}}}

={{{ log((12*12)) - log((6*6*6)) + log((24*24))}}}

={{{ log(((12*12)/(6*6*6))(24*24))}}}............simplify

={{{ log((2*2)/cross(6)*(cross(24)4*24))}}}

={{{ log((2*2*2^2*2^3*3))}}}

={{{ log((2^7*3))}}}

={{{ log((2^7))+log((3))}}}

={{{ 7log(2)+log(3)}}}

={{{ 7(0.301)+0.477}}}

={{{ 2.584}}}