What is log_{10}(5)-log_{10}(20) ?

The solution to log_{10}(5)-log_{10}(20) is -2log_{10}(2)

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simplify log_{10}(5)-log_{10}(20)

simplify

lo g_{10} (5) - lo g_{10} (20)

- 2 lo g_{10} (2)

Decimal Notation

- 0.60205 \dots

Solution steps

lo g_{10} (5) - lo g_{10} (20)

Apply log rule:

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

lo g_{10} (5) - lo g_{10} (20) = lo g_{10} (\frac{5}{20})

= lo g_{10} (\frac{5}{20})

Cancel the numbers:

\frac{5}{20} = \frac{1}{4}

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

\frac{1}{4} = 4^{- 1}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= - 1 \cdot lo g_{10} (4)

Apply rule:

1 \cdot a = a

= - lo g_{10} (4)

Factor the number:

4 = 2^{2}

= - lo g_{10} (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

- lo g_{10} (2^{2}) = - 2 lo g_{10} (2)

= - 2 lo g_{10} (2)

2 \cdot lo g_{10} (x - 4) + lo g_{10} (3 x)

3 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (3 x^{4} y^{- 7})

ln (x y z^{2})

ln (2 + 1) - ln (2 - 1)

What is log_{10}(5)-log_{10}(20) ?
The solution to log_{10}(5)-log_{10}(20) is -2log_{10}(2)