What is log_{10}(24)-log_{10}(6) ?

The solution to log_{10}(24)-log_{10}(6) is 2log_{10}(2)

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simplify log_{10}(24)-log_{10}(6)

simplify

lo g_{10} (24) - lo g_{10} (6)

2 lo g_{10} (2)

Decimal Notation

0.60205 \dots

Solution steps

lo g_{10} (24) - lo g_{10} (6)

Apply log rule:

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

lo g_{10} (24) - lo g_{10} (6) = lo g_{10} (\frac{24}{6})

= lo g_{10} (\frac{24}{6})

Divide the numbers:

\frac{24}{6} = 4

= 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)

lo g_{10} (24) - lo g_{10} (4)

- (\frac{4}{6} \cdot lo g_{2} (\frac{4}{6}) + \frac{2}{6} \cdot lo g_{2} (\frac{2}{6}))

lo g_{7} (\frac{1}{343} x)

4 lo g_{2} (3 x)

lo g_{10} (24) - lo g_{10} (2)

What is log_{10}(24)-log_{10}(6) ?
The solution to log_{10}(24)-log_{10}(6) is 2log_{10}(2)