Solve { \frac {37}{2} \ln |x^4| -\frac {27}{2}\ln |x|

Evaluate

\frac{37}{2} ln (x^{4}) - \frac{27}{2} ln (∣ x ∣) - \frac{21}{x} \times c

When the expression in absolute value bars is not negative, remove the bars

\frac{37}{2} ln (x^{4}) - \frac{27}{2} ln (∣ x ∣) - \frac{21}{x} \times c

Multiply the terms

\frac{37}{2} ln (x^{4}) - \frac{27}{2} ln (∣ x ∣) - \frac{21 c}{x}

Subtract the terms

More Steps

ln (\frac{x ^{74}}{∣ x ∣ ^{\frac{27}{2}}}) - \frac{21 c}{x}

Reduce fractions to a common denominator

\frac{ln ( \frac{x ^{74}}{∣ x ∣ ^{\frac{27}{2}}} ) \times x}{x} - \frac{21 c}{x}

Write all numerators above the common denominator

\frac{ln ( \frac{x ^{74}}{∣ x ∣ ^{\frac{27}{2}}} ) \times x - 21 c}{x}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

More Steps

\frac{ln ( \frac{x ^{74}}{∣ x ^{27} ∣} ) \times x - 21 c}{x}

Solution

\frac{x ln ( \frac{x ^{74}}{∣ x ^{27} ∣} ) - 21 c}{x}

Alternative Form

\frac{148 x ln ( x ) - x ln ( x ^{27} ) - 42 c}{2 x}

Simplify the expression