What is 1/4 log_{10}(33)+1/4 log_{10}(44) ?

The solution to 1/4 log_{10}(33)+1/4 log_{10}(44) is log_{10}(\sqrt[4]{3}sqrt(22))

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simplify 1/4 log_{10}(33)+1/4 log_{10}(44)

simplify

\frac{1}{4} lo g_{10} (33) + \frac{1}{4} lo g_{10} (44)

Decimal Notation

0.79049 \dots

Solution steps

\frac{1}{4} lo g_{10} (33) + \frac{1}{4} lo g_{10} (44)

Apply log rule:

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

\frac{1}{4} lo g_{10} (33) = lo g_{10} (3 3^{\frac{1}{4}})

= lo g_{10} (3 3^{\frac{1}{4}}) + \frac{1}{4} lo g_{10} (44)

Apply log rule:

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

\frac{1}{4} lo g_{10} (44) = lo g_{10} (4 4^{\frac{1}{4}})

= lo g_{10} (3 3^{\frac{1}{4}}) + lo g_{10} (4 4^{\frac{1}{4}})

Apply log rule:

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

lo g_{10} (3 3^{\frac{1}{4}}) + lo g_{10} (4 4^{\frac{1}{4}}) = lo g_{10} (3 3^{\frac{1}{4}} \cdot 4 4^{\frac{1}{4}})

= lo g_{10} (3 3^{\frac{1}{4}} \cdot 4 4^{\frac{1}{4}})

lo g_{b} (8 k)

lo g_{10} (1000 x)

lo g_{3} (x^{2} - 1) - lo g_{3} (x + 1)

\frac{1}{3} [5 ln (x + 6) - ln (x) - ln (x^{2} - 25)]

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

What is 1/4 log_{10}(33)+1/4 log_{10}(44) ?
The solution to 1/4 log_{10}(33)+1/4 log_{10}(44) is log_{10}(\sqrt[4]{3}sqrt(22))