What is 2log_{4}(11)-10log_{4}(10) ?

The solution to 2log_{4}(11)-10log_{4}(10) is log_{4}((121)/(10^{10)})

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simplify 2log_{4}(11)-10log_{4}(10)

simplify

2 lo g_{4} (11) - 10 lo g_{4} (10)

lo g_{4} (\frac{121}{1 0 ^{10}})

Decimal Notation

- 13.15020 \dots

Solution steps

2 lo g_{4} (11) - 10 lo g_{4} (10)

2 lo g_{4} (11) = lo g_{4} (1 1^{2})

- 10 lo g_{4} (10) = - lo g_{4} (1 0^{10})

= lo g_{4} (1 1^{2}) - lo g_{4} (1 0^{10})

Apply log rule:

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

lo g_{4} (1 1^{2}) - lo g_{4} (1 0^{10}) = lo g_{4} (\frac{1 1 ^{2}}{1 0 ^{10}})

= lo g_{4} (\frac{1 1 ^{2}}{1 0 ^{10}})

1 1^{2} = 121

= lo g_{4} (\frac{121}{1 0 ^{10}})

3 ln (x) - ln (3 x) + ln (12 x^{2})

ln (x^{2}) - 2 ln (y)

lo g_{10} (x y^{5})

lo g_{10} (x^{5} y^{4})

lo g_{5} (\frac{100}{3 x})

What is 2log_{4}(11)-10log_{4}(10) ?
The solution to 2log_{4}(11)-10log_{4}(10) is log_{4}((121)/(10^{10)})