What is log_{10}(((3b^2+21b))/((11b+77))) ?

The solution to log_{10}(((3b^2+21b))/((11b+77))) is log_{10}(3)+log_{10}(b)-log_{10}(11)

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simplify log_{10}(((3b^2+21b))/((11b+77)))

simplify

lo g_{10} (\frac{( 3 b ^{2} + 21 b )}{( 11 b + 77 )})

lo g_{10} (3) + lo g_{10} (b) - lo g_{10} (11)

Solution steps

lo g_{10} (\frac{3 b ^{2} + 21 b}{11 b + 77})

Simplify

\frac{3 b ^{2} + 21 b}{11 b + 77} : \frac{3 b}{11}

= lo g_{10} (\frac{3 b}{11})

Apply log rule:

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

lo g_{10} (\frac{3 b}{11}) = lo g_{10} (3 b) - lo g_{10} (11)

= lo g_{10} (3 b) - lo g_{10} (11)

Simplify

lo g_{10} (3 b) : lo g_{10} (3) + lo g_{10} (b)

= lo g_{10} (3) + lo g_{10} (b) - lo g_{10} (11)

lo g_{10} (\frac{9 x ^{5}}{y ^{6}})

lo g_{10} (6) - 2 lo g_{10} (y)

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

lo g_{b} (6) - lo g_{b} (3)

lo g_{7} (3 x) - lo g_{7} (9 x) + lo g_{7} (6 y)

What is log_{10}(((3b^2+21b))/((11b+77))) ?
The solution to log_{10}(((3b^2+21b))/((11b+77))) is log_{10}(3)+log_{10}(b)-log_{10}(11)