What is 1/2*log_{10}(2)+log_{10}(3) ?

The solution to 1/2*log_{10}(2)+log_{10}(3) is log_{10}(2^{1/2}*3)

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simplify 1/2*log_{10}(2)+log_{10}(3)

simplify

\frac{1}{2} \cdot lo g_{10} (2) + lo g_{10} (3)

lo g_{10} (2^{\frac{1}{2}} \cdot 3)

Decimal Notation

0.62763 \dots

Solution steps

\frac{1}{2} lo g_{10} (2) + lo g_{10} (3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (2) = lo g_{10} (2^{\frac{1}{2}})

= lo g_{10} (2^{\frac{1}{2}}) + lo g_{10} (3)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (2^{\frac{1}{2}}) + lo g_{10} (3) = lo g_{10} (3 \cdot 2^{\frac{1}{2}})

= lo g_{10} (2^{\frac{1}{2}} \cdot 3)

ln (3 x) - ln (\frac{1}{2} x)

lo g_{b} (\frac{x ^{3} y}{z ^{6}})

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

3 ln (x) + 3 ln (y)

lo g_{10} (x^{2}) y^{2}

What is 1/2*log_{10}(2)+log_{10}(3) ?
The solution to 1/2*log_{10}(2)+log_{10}(3) is log_{10}(2^{1/2}*3)