What is 4(-ln(e^3z^{5/2})+ln((x^3)/(y^2))) ?

The solution to 4(-ln(e^3z^{5/2})+ln((x^3)/(y^2))) is 4ln((x^3)/(e^3y^2z^{5/2)})

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simplify 4(-ln(e^3z^{5/2})+ln((x^3)/(y^2)))

simplify

4 (- ln (e^{3} z^{\frac{5}{2}}) + ln (\frac{x ^{3}}{y ^{2}}))

4 ln (\frac{x ^{3}}{e ^{3} y ^{2} z ^{\frac{5}{2}}})

Solution steps

4 (- ln (e^{3} z^{\frac{5}{2}}) + ln (\frac{x ^{3}}{y ^{2}}))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{x ^{3}}{y ^{2}}) - ln (e^{3} z^{\frac{5}{2}}) = ln (\frac{\frac{x ^{3}}{y ^{2}}}{e ^{3} z ^{\frac{5}{2}}})

= 4 (ln (\frac{\frac{x ^{3}}{y ^{2}}}{e ^{3} z ^{\frac{5}{2}}}))

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= 4 (ln (\frac{x ^{3}}{e ^{3} y ^{2} z ^{\frac{5}{2}}}))

Remove parentheses:

(a) = a

= 4 ln (\frac{x ^{3}}{e ^{3} y ^{2} z ^{\frac{5}{2}}})

\frac{12 ln ( 3 )}{ln ( 20 )} - 1

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- (\frac{3}{7} lo g_{2} (\frac{3}{7}) + \frac{4}{7} lo g_{2} (\frac{4}{7}))

What is 4(-ln(e^3z^{5/2})+ln((x^3)/(y^2))) ?
The solution to 4(-ln(e^3z^{5/2})+ln((x^3)/(y^2))) is 4ln((x^3)/(e^3y^2z^{5/2)})