What is expand ((1+t)*ln|x|)-((1+3t)*ln|y|) ?

The solution to expand ((1+t)*ln|x|)-((1+3t)*ln|y|) is ln|x|+tln|x|-ln|y|-3tln|y|

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expand ((1+t)ln|x|)-((1+3t)ln|y|)

expand

((1 + t) \cdot ln ∣ x ∣) - ((1 + 3 t) \cdot ln ∣ y ∣)

ln ∣ x ∣ + t ln ∣ x ∣ - ln ∣ y ∣ - 3 t ln ∣ y ∣

Solution steps

((1 + t) ln ∣ x ∣) - ((1 + 3 t) ln ∣ y ∣)

Remove parentheses:

(a) = a

= (1 + t) ln ∣ x ∣ - (1 + 3 t) ln ∣ y ∣

= ln ∣ x ∣ (1 + t) - ln ∣ y ∣ (1 + 3 t)

Expand

ln ∣ x ∣ (1 + t) : ln ∣ x ∣ + t ln ∣ x ∣

= ln ∣ x ∣ + t ln ∣ x ∣ - (1 + 3 t) ln ∣ y ∣

Expand

- ln ∣ y ∣ (1 + 3 t) : - ln ∣ y ∣ - 3 t ln ∣ y ∣

= ln ∣ x ∣ + t ln ∣ x ∣ - ln ∣ y ∣ - 3 t ln ∣ y ∣

\frac{2 x}{( x ^{2} + 1 ) ^{3}}

\frac{s}{( s ^{2} + 2 ) ( s ^{4} - 2 s - 1 )}

(e^{x} + 1)^{15}

\frac{3 ( 8 - x ^{2} ) ^{2}}{2}

\frac{a ^{2} + ab}{( a - b ) ^{2}}

What is expand ((1+t)*ln|x|)-((1+3t)*ln|y|) ?
The solution to expand ((1+t)*ln|x|)-((1+3t)*ln|y|) is ln|x|+tln|x|-ln|y|-3tln|y|