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

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

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simplify log_{7}(7mn^4)

simplify

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_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{7} (7) = 1

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

Simplify

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

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

Apply rule:

a + (b + c) = a + b + c

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

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

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

\frac{1}{2} lo g_{2} (127)

- lo g_{10} (3.1 \cdot 1 0^{- 5})

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

lo g_{4} (\frac{7}{19}) + lo g_{4} (\frac{19}{7})

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