What is log_{4}(16)-log_{4}(20)-log_{4}(5) ?

The solution to log_{4}(16)-log_{4}(20)-log_{4}(5) is log_{4}(4/25)

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simplify log_{4}(16)-log_{4}(20)-log_{4}(5)

simplify

lo g_{4} (16) - lo g_{4} (20) - lo g_{4} (5)

lo g_{4} (\frac{4}{25})

Decimal Notation

- 1.32192 \dots

Solution steps

lo g_{4} (16) - lo g_{4} (20) - lo g_{4} (5)

Apply log rule:

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

lo g_{4} (16) - lo g_{4} (20) = lo g_{4} (\frac{16}{20})

= lo g_{4} (\frac{16}{20}) - lo g_{4} (5)

Apply log rule:

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

lo g_{4} (\frac{16}{20}) - lo g_{4} (5) = lo g_{4} (\frac{\frac{16}{20}}{5})

= lo g_{4} (\frac{\frac{16}{20}}{5})

\frac{\frac{16}{20}}{5} = \frac{4}{25}

= lo g_{4} (\frac{4}{25})

ln (\frac{1}{36})

lo g_{8} (3 x - 1) - 5 lo g_{8} (x)

lo g_{10} (3) - lo g_{10} (12)

3 ln (2) - ln (5)

lo g_{2} (x) - lo g_{2} (x - 3)

What is log_{4}(16)-log_{4}(20)-log_{4}(5) ?
The solution to log_{4}(16)-log_{4}(20)-log_{4}(5) is log_{4}(4/25)