I've been having trouble with this question.
Expand as the sum of the individual logarithms, each of whose argument is linear?:
$${{log}}_{{\mathtt{5}}}{\left({\frac{{\mathtt{24}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{3}}}]{{{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{y}}}^{{\mathtt{5}}}}}}{{{\mathtt{z}}}^{-{\mathtt{2}}}}}\right)}$$
+130511 We can write this as
log5 ( 24z2 * x4/3 y5/3).......and by a log property we can write
log5 ( 24z2 ) + log5 ( x4/3 y5/3 ) .......and by applying the property again, we have
log5(24) + log5 (z2) + log5( x4/3 ) + log5 ( y5/3 )... .....we can simpify it further using another log property.....
log5(24) + 2 log5 (z) + (4/3) log5 (x) + (5/3) log5 (y) ......this is linear (without exponents)......
(Using the "change of base" rule, you could write the first term as a decimal approximation, but I might just keep it as is)
+130511 We can write this as
log5 ( 24z2 * x4/3 y5/3).......and by a log property we can write
log5 ( 24z2 ) + log5 ( x4/3 y5/3 ) .......and by applying the property again, we have
log5(24) + log5 (z2) + log5( x4/3 ) + log5 ( y5/3 )... .....we can simpify it further using another log property.....
log5(24) + 2 log5 (z) + (4/3) log5 (x) + (5/3) log5 (y) ......this is linear (without exponents)......
(Using the "change of base" rule, you could write the first term as a decimal approximation, but I might just keep it as is)
