What is expand log_{7}((6x)/(y^2)) ?

The solution to expand log_{7}((6x)/(y^2)) is log_{7}(6)+log_{7}(x)-2log_{7}(y)

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expand log_{7}((6x)/(y^2))

expand

lo g_{7} (\frac{6 x}{y ^{2}})

lo g_{7} (6) + lo g_{7} (x) - 2 lo g_{7} (y)

Solution steps

lo g_{7} (\frac{6 x}{y ^{2}})

Apply log rule:

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

lo g_{7} (\frac{6 x}{y ^{2}}) = lo g_{7} (6 x) - lo g_{7} (y^{2})

= lo g_{7} (6 x) - lo g_{7} (y^{2})

Apply log rule:

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

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

= lo g_{7} (6 x) - 2 lo g_{7} (y)

Apply log rule:

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

lo g_{7} (6 x) = lo g_{7} (6) + lo g_{7} (x)

= lo g_{7} (6) + lo g_{7} (x) - 2 lo g_{7} (y)

\frac{1}{2} lo g_{10} (- 2 lo g_{10} (y))

lo g_{7} (49 x^{2})

\frac{48}{343 ln ( 7 )} + \frac{1}{e} - \frac{1}{e ^{3}}

4 lo g_{10} (a) - 2 lo g_{10} (b)

ln (20.5) - ln (20)

What is expand log_{7}((6x)/(y^2)) ?
The solution to expand log_{7}((6x)/(y^2)) is log_{7}(6)+log_{7}(x)-2log_{7}(y)