What is log_{10}(2)+5log_{10}(3) ?

The solution to log_{10}(2)+5log_{10}(3) is log_{10}(486)

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simplify log_{10}(2)+5log_{10}(3)

simplify

lo g_{10} (2) + 5 lo g_{10} (3)

lo g_{10} (486)

Decimal Notation

2.68663 \dots

Solution steps

lo g_{10} (2) + 5 lo g_{10} (3)

Apply log rule:

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

5 lo g_{10} (3) = lo g_{10} (3^{5})

= lo g_{10} (2) + lo g_{10} (3^{5})

Apply log rule:

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

lo g_{10} (2) + lo g_{10} (3^{5}) = lo g_{10} (2 \cdot 3^{5})

= lo g_{10} (2 \cdot 3^{5})

2 \cdot 3^{5} = 486

= lo g_{10} (486)

ln (x 2 x + 1)

lo g_{10} (\frac{y ^{8}}{3 x})

lo g_{10} (\frac{( y ^{2} )}{2 z})

lo g_{6} (\frac{f}{36})

ln (\frac{x ^{4} + 1}{x + 1})

What is log_{10}(2)+5log_{10}(3) ?
The solution to log_{10}(2)+5log_{10}(3) is log_{10}(486)