What is log_{b}((by^5)/(m^2n^4)) ?

The solution to log_{b}((by^5)/(m^2n^4)) is 1+5log_{b}(y)-2log_{b}(m)-4log_{b}(n)

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simplify log_{b}((by^5)/(m^2n^4))

simplify

lo g_{b} (\frac{b y ^{5}}{m ^{2} n ^{4}})

1 + 5 lo g_{b} (y) - 2 lo g_{b} (m) - 4 lo g_{b} (n)

Solution steps

lo g_{b} (\frac{b y ^{5}}{m ^{2} n ^{4}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{b} (\frac{b y ^{5}}{m ^{2} n ^{4}}) = lo g_{b} (b y^{5}) - lo g_{b} (m^{2} n^{4})

= lo g_{b} (b y^{5}) - lo g_{b} (m^{2} n^{4})

lo g_{b} (b y^{5}) = 1 + 5 lo g_{b} (y)

lo g_{b} (m^{2} n^{4}) = 2 lo g_{b} (m) + 4 lo g_{b} (n)

= 1 + 5 lo g_{b} (y) - (2 lo g_{b} (m) + 4 lo g_{b} (n))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{b} (m) + 4 lo g_{b} (n)) = - 2 lo g_{b} (m) - 4 lo g_{b} (n)

= 1 + 5 lo g_{b} (y) - 2 lo g_{b} (m) - 4 lo g_{b} (n)

\frac{1}{5} lo g_{4} (w) + 4 lo g_{4} (z) - lo g_{4} (y)

ln (x^{7} 5 - x)

800 ln (10) - 480 ln (6) - 320

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

lo g_{10} (\frac{x ^{5}}{y ^{3}})

What is log_{b}((by^5)/(m^2n^4)) ?
The solution to log_{b}((by^5)/(m^2n^4)) is 1+5log_{b}(y)-2log_{b}(m)-4log_{b}(n)