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

The solution to 2log_{10}(3)-3log_{10}(2) is log_{10}(9/8)

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

simplify

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

lo g_{10} (\frac{9}{8})

Decimal Notation

0.05115 \dots

Solution steps

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

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

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

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

Apply log rule:

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

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

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

\frac{3 ^{2}}{2 ^{3}} = \frac{9}{8}

= lo g_{10} (\frac{9}{8})

ln (5) + ln (2)

1 - lo g_{4} (m - 1) - lo g_{4} (m + 1)

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

ln (\frac{x + y}{x - y})

2 [3 ln (x) - ln (x + 1) - ln (x - 1)]

What is 2log_{10}(3)-3log_{10}(2) ?
The solution to 2log_{10}(3)-3log_{10}(2) is log_{10}(9/8)