What is 4log_{10}(3)-6log_{10}(2) ?

The solution to 4log_{10}(3)-6log_{10}(2) is log_{10}(81/64)

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simplify 4log_{10}(3)-6log_{10}(2)

simplify

4 lo g_{10} (3) - 6 lo g_{10} (2)

lo g_{10} (\frac{81}{64})

Decimal Notation

0.10230 \dots

Solution steps

4 lo g_{10} (3) - 6 lo g_{10} (2)

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

- 6 lo g_{10} (2) = - lo g_{10} (2^{6})

= lo g_{10} (3^{4}) - lo g_{10} (2^{6})

Apply log rule:

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

lo g_{10} (3^{4}) - lo g_{10} (2^{6}) = lo g_{10} (\frac{3 ^{4}}{2 ^{6}})

= lo g_{10} (\frac{3 ^{4}}{2 ^{6}})

\frac{3 ^{4}}{2 ^{6}} = \frac{81}{64}

= lo g_{10} (\frac{81}{64})

lo g_{4} (12 x^{3})

ln (\frac{5}{2 x ^{2} y})

3 ln (x) + ln (y)

lo g_{4} (\frac{16}{x + 2})

What is 4log_{10}(3)-6log_{10}(2) ?
The solution to 4log_{10}(3)-6log_{10}(2) is log_{10}(81/64)