What is 3log_{10}(20.9)-log_{10}(30) ?

The solution to 3log_{10}(20.9)-log_{10}(30) is log_{10}(304.31096…)

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simplify 3log_{10}(20.9)-log_{10}(30)

simplify

3 lo g_{10} (20.9) - lo g_{10} (30)

lo g_{10} (304.31096 \dots)

Decimal Notation

2.48331 \dots

Solution steps

3 lo g_{10} (20.9) - lo g_{10} (30)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{10} (20.9) = lo g_{10} (20. 9^{3})

= lo g_{10} (20. 9^{3}) - lo g_{10} (30)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (20. 9^{3}) - lo g_{10} (30) = lo g_{10} (\frac{20. 9 ^{3}}{30})

= lo g_{10} (\frac{20. 9 ^{3}}{30})

\frac{20. 9 ^{3}}{30} = 304.31096 \dots

= lo g_{10} (304.31096 \dots)

2.45 + lo g_{10} (\frac{0.055}{0.059})

\frac{1}{5} lo g_{8} (18)

92.44 + 20 \cdot lo g_{10} (7.54 \cdot 2.17)

7^{l o g_{7} (4 - 2) l o g_{7} (2)} + 3^{l o g_{3} (5) + l o g_{3} (2)} - 2 ln (e^{3})

\frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

What is 3log_{10}(20.9)-log_{10}(30) ?
The solution to 3log_{10}(20.9)-log_{10}(30) is log_{10}(304.31096…)