What is log_{7}(1/49 mn^2) ?

The solution to log_{7}(1/49 mn^2) is -2+log_{7}(m)+2log_{7}(n)

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simplify log_{7}(1/49 mn^2)

simplify

lo g_{7} (\frac{1}{49} m n^{2})

- 2 + lo g_{7} (m) + 2 lo g_{7} (n)

Solution steps

lo g_{7} (\frac{1}{49} m n^{2})

\frac{1}{49} = 7^{- 2}

= lo g_{7} (7^{- 2} m n^{2})

Apply log rule:

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

lo g_{7} (7^{- 2} m n^{2}) = lo g_{7} (7^{- 2}) + lo g_{7} (m n^{2})

= lo g_{7} (7^{- 2}) + lo g_{7} (m n^{2})

Apply log rule:

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

lo g_{7} (7^{- 2}) = - 2

= - 2 + lo g_{7} (m n^{2})

Simplify

lo g_{7} (m n^{2}) : lo g_{7} (m) + 2 lo g_{7} (n)

= - 2 + (lo g_{7} (m) + 2 lo g_{7} (n))

Apply rule:

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

- 2 + (lo g_{7} (m) + 2 lo g_{7} (n)) = - 2 + lo g_{7} (m) + 2 lo g_{7} (n)

= - 2 + lo g_{7} (m) + 2 lo g_{7} (n)

lo g_{10} (\frac{1}{c})

3 ln (x) - 5 ln (y) - \frac{1}{4} ln (x)

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )})

lo g_{2} (\frac{1}{2} x^{2} y)

What is log_{7}(1/49 mn^2) ?
The solution to log_{7}(1/49 mn^2) is -2+log_{7}(m)+2log_{7}(n)