What is ln((d^2+3h^2)/(6h)) ?

The solution to ln((d^2+3h^2)/(6h)) is ln(d^2+3h^2)-ln(6)-ln(h)

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simplify ln((d^2+3h^2)/(6h))

simplify

ln (\frac{d ^{2} + 3 h ^{2}}{6 h})

ln (d^{2} + 3 h^{2}) - ln (6) - ln (h)

Solution steps

ln (\frac{d ^{2} + 3 h ^{2}}{6 h})

Apply log rule:

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

ln (\frac{d ^{2} + 3 h ^{2}}{6 h}) = ln (d^{2} + 3 h^{2}) - ln (6 h)

= ln (d^{2} + 3 h^{2}) - ln (6 h)

Apply log rule:

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

ln (6 h) = ln (6) + ln (h)

= ln (d^{2} + 3 h^{2}) - (ln (h) + ln (6))

- (ln (6) + ln (h)) : - ln (6) - ln (h)

= ln (d^{2} + 3 h^{2}) - ln (6) - ln (h)

\frac{2}{5} ln (\frac{3}{7})

- ln (x) + ln (\frac{2 y + x}{x})

- 5 ln (\frac{a}{c}) - 8 ln (\frac{c}{a})

ln (x y^{x})

lo g_{b} (\frac{25}{x + 7})

What is ln((d^2+3h^2)/(6h)) ?
The solution to ln((d^2+3h^2)/(6h)) is ln(d^2+3h^2)-ln(6)-ln(h)