What is 3ln(a)-1/2 (ln(b)+ln(c^2)) ?

The solution to 3ln(a)-1/2 (ln(b)+ln(c^2)) is ln((a^3sqrt(b))/(bc))

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simplify 3ln(a)-1/2 (ln(b)+ln(c^2))

simplify

3 ln (a) - \frac{1}{2} (ln (b) + ln (c^{2}))

ln (\frac{a ^{3} b}{b c})

Solution steps

3 ln (a) - \frac{1}{2} (ln (b) + ln (c^{2}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (b) + ln (c^{2}) = ln (b c^{2})

= 3 ln (a) - \frac{1}{2} ln (b c^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (a) = ln (a^{3})

= ln (a^{3}) - \frac{1}{2} ln (b c^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (b c^{2}) = ln ((b c^{2})^{\frac{1}{2}})

= ln (a^{3}) - ln ((b c^{2})^{\frac{1}{2}})

Apply log rule:

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

ln (a^{3}) - ln ((b c^{2})^{\frac{1}{2}}) = ln (\frac{a ^{3}}{( b c ^{2} ) ^{\frac{1}{2}}})

= ln (\frac{a ^{3}}{( b c ^{2} ) ^{\frac{1}{2}}})

Simplify

\frac{a ^{3}}{( b c ^{2} ) ^{\frac{1}{2}}} : \frac{a ^{3} b}{b c}

= ln (\frac{a ^{3} b}{b c})

ln (\frac{1}{y})

- 4 ln (3 x)

4 ln (x) - 5 ln (y)

lo g_{10} (7 z)

What is 3ln(a)-1/2 (ln(b)+ln(c^2)) ?
The solution to 3ln(a)-1/2 (ln(b)+ln(c^2)) is ln((a^3sqrt(b))/(bc))