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Popular >

simplify ln(((d-r)^2)/(r^2))

Solution

simplify

ln (\frac{( d - r ) ^{2}}{r ^{2}})

Solution

2 ln (d - r) - 2 ln (r)

Solution steps

ln (\frac{( d - r ) ^{2}}{r ^{2}})

Apply log rule:

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

ln (\frac{( d - r ) ^{2}}{r ^{2}}) = ln ((d - r)^{2}) - ln (r^{2})

= ln ((d - r)^{2}) - ln (r^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((d - r)^{2}) = 2 ln (d - r)

= 2 ln (d - r) - ln (r^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (r^{2}) = 2 ln (r)

= 2 ln (d - r) - 2 ln (r)

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Frequently Asked Questions (FAQ)

What is ln(((d-r)^2)/(r^2)) ?
The solution to ln(((d-r)^2)/(r^2)) is 2ln(d-r)-2ln(r)