What is 4log_{10}(3)+1log_{10}(x) ?

The solution to 4log_{10}(3)+1log_{10}(x) is log_{10}(81x)

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simplify 4log_{10}(3)+1log_{10}(x)

simplify

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

lo g_{10} (81 x)

Solution steps

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

Apply rule:

1 \cdot a = a

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

= 4 lo g_{10} (3) + lo g_{10} (x)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Apply log rule:

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

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

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

Simplify

3^{4} x : 81 x

= lo g_{10} (81 x)

lo g_{4} (\frac{x ^{2} y}{z})

lo g_{10} (x) - 5 lo g_{10} (y) + 6 lo g_{10} (z)

\frac{1}{4} lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (x)

ln (8 x + 4) - 2 ln (2)

lo g_{9} (10) - lo g_{9} (\frac{1}{2}) - lo g_{9} (4)

What is 4log_{10}(3)+1log_{10}(x) ?
The solution to 4log_{10}(3)+1log_{10}(x) is log_{10}(81x)