What is log_{10}(9)+3log_{10}(2)-log_{10}(3) ?

The solution to log_{10}(9)+3log_{10}(2)-log_{10}(3) is log_{10}(24)

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simplify log_{10}(9)+3log_{10}(2)-log_{10}(3)

simplify

lo g_{10} (9) + 3 lo g_{10} (2) - lo g_{10} (3)

lo g_{10} (24)

Decimal Notation

1.38021 \dots

Solution steps

lo g_{10} (9) + 3 lo g_{10} (2) - lo g_{10} (3)

Apply log rule:

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

3 lo g_{10} (2) = lo g_{10} (2^{3})

= lo g_{10} (9) + lo g_{10} (2^{3}) - lo g_{10} (3)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (9) + lo g_{10} (2^{3}) = lo g_{10} (9 \cdot 2^{3})

= lo g_{10} (9 \cdot 2^{3}) - lo g_{10} (3)

Apply log rule:

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

lo g_{10} (9 \cdot 2^{3}) - lo g_{10} (3) = lo g_{10} (\frac{9 \cdot 2 ^{3}}{3})

= lo g_{10} (\frac{9 \cdot 2 ^{3}}{3})

Cancel

\frac{9 \cdot 2 ^{3}}{3} : 24

= lo g_{10} (24)

5 lo g_{10} (x^{3} y) - 3 lo g_{10} (x y^{2})

ln (\frac{10}{100})

lo g_{10} (a) + lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{4} (\frac{16}{x ^{4}})

lo g_{a} (\frac{x ^{8}}{y z ^{9}})

What is log_{10}(9)+3log_{10}(2)-log_{10}(3) ?
The solution to log_{10}(9)+3log_{10}(2)-log_{10}(3) is log_{10}(24)