What is 6log_{10}(3/2)+2log_{10}(2) ?

The solution to 6log_{10}(3/2)+2log_{10}(2) is log_{10}(729/16)

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simplify 6log_{10}(3/2)+2log_{10}(2)

simplify

6 lo g_{10} (\frac{3}{2}) + 2 lo g_{10} (2)

lo g_{10} (\frac{729}{16})

Decimal Notation

1.65860 \dots

Solution steps

6 lo g_{10} (\frac{3}{2}) + 2 lo g_{10} (2)

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

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

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

Apply log rule:

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

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

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

Simplify

(\frac{3}{2})^{6} \cdot 2^{2} : \frac{729}{16}

= lo g_{10} (\frac{729}{16})

lo g_{10} (\frac{x ^{4}}{y ^{5}})

lo g_{4} (\frac{16}{x + 6})

4 ln (x) + 5 ln (y) - 2 ln (z)

ln (\frac{9}{8 x ^{8} y})

lo g_{8} (7) - lo g_{8} (5)

What is 6log_{10}(3/2)+2log_{10}(2) ?
The solution to 6log_{10}(3/2)+2log_{10}(2) is log_{10}(729/16)