What is expand log_{7}(7mn^4) ?

The solution to expand log_{7}(7mn^4) is 1+log_{7}(m)+4log_{7}(n)

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expand log_{7}(7mn^4)

expand

lo g_{7} (7 m n^{4})

1 + lo g_{7} (m) + 4 lo g_{7} (n)

Solution steps

lo g_{7} (7 m n^{4})

Apply log rule:

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

lo g_{7} (7 m n^{4}) = lo g_{7} (7) + lo g_{7} (m) + lo g_{7} (n^{4})

= lo g_{7} (7) + lo g_{7} (m) + lo g_{7} (n^{4})

Apply log rule:

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

lo g_{7} (n^{4}) = 4 lo g_{7} (n)

= lo g_{7} (7) + lo g_{7} (m) + 4 lo g_{7} (n)

Apply log rule:

lo g_{a} (a) = 1

= 1 + lo g_{7} (m) + 4 lo g_{7} (n)

lo g_{10} (\frac{a b ^{7}}{c ^{8}})

lo g_{2} (A B^{2})

ln (\frac{( 3 ^{x} 6 ^{2 x} )}{2 ^{2 x}})

lo g_{6} (\frac{1}{z ^{3}})

ln (e^{x} x)

What is expand log_{7}(7mn^4) ?
The solution to expand log_{7}(7mn^4) is 1+log_{7}(m)+4log_{7}(n)