What is 3log_{10}(9)+1log_{10}(x) ?

The solution to 3log_{10}(9)+1log_{10}(x) is log_{10}(729x)

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simplify 3log_{10}(9)+1log_{10}(x)

simplify

3 lo g_{10} (9) + 1 lo g_{10} (x)

lo g_{10} (729 x)

Solution steps

3 lo g_{10} (9) + 1 \cdot lo g_{10} (x)

3 lo g_{10} (9) = lo g_{10} (9^{3})

1 \cdot lo g_{10} (x) = lo g_{10} (x^{1})

= lo g_{10} (9^{3}) + lo g_{10} (x^{1})

Apply log rule:

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

lo g_{10} (9^{3}) + lo g_{10} (x^{1}) = lo g_{10} (9^{3} x^{1})

= lo g_{10} (9^{3} x^{1})

Simplify

9^{3} x^{1} : 729 x

= lo g_{10} (729 x)

ln (5) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

3 lo g_{5} (\frac{u v ^{2}}{w ^{3}})

\frac{1}{2} lo g_{10} (24) - lo g_{10} (4)

lo g_{b} (x^{3} \frac{y ^{2}}{z})

What is 3log_{10}(9)+1log_{10}(x) ?
The solution to 3log_{10}(9)+1log_{10}(x) is log_{10}(729x)