What is log_{10}((sqrt((m-n)(m+n)))/((m-n)^2)) ?

The solution to log_{10}((sqrt((m-n)(m+n)))/((m-n)^2)) is log_{10}(sqrt((m-n)(m+n)))-2log_{10}(m-n)

Popular >

simplify log_{10}((sqrt((m-n)(m+n)))/((m-n)^2))

simplify

lo g_{10} (\frac{( m - n ) ( m + n )}{( m - n ) ^{2}})

lo g_{10} ((m - n) (m + n)) - 2 lo g_{10} (m - n)

Solution steps

lo g_{10} (\frac{( m - n ) ( m + n )}{( m - n ) ^{2}})

Apply log rule:

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

lo g_{10} (\frac{( m - n ) ( m + n )}{( m - n ) ^{2}}) = lo g_{10} ((m - n) (m + n)) - lo g_{10} ((m - n)^{2})

= lo g_{10} ((m - n) (m + n)) - lo g_{10} ((m - n)^{2})

Apply log rule:

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

lo g_{10} ((m - n)^{2}) = 2 lo g_{10} (m - n)

= lo g_{10} ((m - n) (m + n)) - 2 lo g_{10} (m - n)

(\frac{1}{2}) ln (4 t^{4}) - ln (2)

- lo g_{10} (2.5 \cdot 1 0^{- 1})

3 ln (2 x^{3})

lo g_{e} (5 e^{- 2})

lo g_{e} (\frac{1}{3 - x})

What is log_{10}((sqrt((m-n)(m+n)))/((m-n)^2)) ?
The solution to log_{10}((sqrt((m-n)(m+n)))/((m-n)^2)) is log_{10}(sqrt((m-n)(m+n)))-2log_{10}(m-n)