What is ln(a^2-b^2)-5ln(c) ?

The solution to ln(a^2-b^2)-5ln(c) is ln((a^2-b^2)/(c^5))

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simplify ln(a^2-b^2)-5ln(c)

simplify

ln (a^{2} - b^{2}) - 5 ln (c)

ln (\frac{a ^{2} - b ^{2}}{c ^{5}})

Solution steps

ln (a^{2} - b^{2}) - 5 ln (c)

Apply log rule:

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

5 ln (c) = ln (c^{5})

= ln (a^{2} - b^{2}) - ln (c^{5})

Apply log rule:

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

ln (a^{2} - b^{2}) - ln (c^{5}) = ln (\frac{a ^{2} - b ^{2}}{c ^{5}})

= ln (\frac{a ^{2} - b ^{2}}{c ^{5}})

ln (\frac{25}{x})

ln (\frac{2}{3 \cdot e ^{x} + c})

\frac{1}{2} ln (1 + x^{2}) - ln (x)

lo g_{e} (x sin (x))

\frac{125}{3} ln (2)

What is ln(a^2-b^2)-5ln(c) ?
The solution to ln(a^2-b^2)-5ln(c) is ln((a^2-b^2)/(c^5))