What is 2log_{10}(4)-3log_{10}(3) ?

The solution to 2log_{10}(4)-3log_{10}(3) is log_{10}(16/27)

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simplify 2log_{10}(4)-3log_{10}(3)

simplify

2 lo g_{10} (4) - 3 lo g_{10} (3)

lo g_{10} (\frac{16}{27})

Decimal Notation

- 0.22724 \dots

Solution steps

2 lo g_{10} (4) - 3 lo g_{10} (3)

2 lo g_{10} (4) = lo g_{10} (4^{2})

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

= lo g_{10} (4^{2}) - lo g_{10} (3^{3})

Apply log rule:

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

lo g_{10} (4^{2}) - lo g_{10} (3^{3}) = lo g_{10} (\frac{4 ^{2}}{3 ^{3}})

= lo g_{10} (\frac{4 ^{2}}{3 ^{3}})

\frac{4 ^{2}}{3 ^{3}} = \frac{16}{27}

= lo g_{10} (\frac{16}{27})

ln (x^{4} 2 - x)

ln (\frac{3 a ^{2} b ^{2}}{a})

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

lo g_{7} (2 \cdot 6) + lo g_{7} (3)

- \frac{1}{14} ln ∣ 3 x - 1 ∣ - 3 ln ∣ 3 - 2 ∣ + \frac{32}{7} ln ∣ 3 + 3 ∣

What is 2log_{10}(4)-3log_{10}(3) ?
The solution to 2log_{10}(4)-3log_{10}(3) is log_{10}(16/27)