What is log_{9}(6)+1/2*log_{9}(a)+1/2*log_{9}(b) ?

The solution to log_{9}(6)+1/2*log_{9}(a)+1/2*log_{9}(b) is log_{9}(6a^{1/2}b^{1/2})

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simplify log_{9}(6)+1/2log_{9}(a)+1/2log_{9}(b)

simplify

lo g_{9} (6) + \frac{1}{2} \cdot lo g_{9} (a) + \frac{1}{2} \cdot lo g_{9} (b)

lo g_{9} (6 a^{\frac{1}{2}} b^{\frac{1}{2}})

Solution steps

lo g_{9} (6) + \frac{1}{2} lo g_{9} (a) + \frac{1}{2} lo g_{9} (b)

Apply log rule:

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

\frac{1}{2} lo g_{9} (a) = lo g_{9} (a^{\frac{1}{2}})

= lo g_{9} (6) + lo g_{9} (a^{\frac{1}{2}}) + \frac{1}{2} lo g_{9} (b)

Apply log rule:

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

lo g_{9} (6) + lo g_{9} (a^{\frac{1}{2}}) = lo g_{9} (6 a^{\frac{1}{2}})

= lo g_{9} (6 a^{\frac{1}{2}}) + \frac{1}{2} lo g_{9} (b)

Apply log rule:

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

\frac{1}{2} lo g_{9} (b) = lo g_{9} (b^{\frac{1}{2}})

= lo g_{9} (6 a^{\frac{1}{2}}) + lo g_{9} (b^{\frac{1}{2}})

Apply log rule:

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

lo g_{9} (6 a^{\frac{1}{2}}) + lo g_{9} (b^{\frac{1}{2}}) = lo g_{9} (6 a^{\frac{1}{2}} b^{\frac{1}{2}})

= lo g_{9} (6 a^{\frac{1}{2}} b^{\frac{1}{2}})

\frac{1}{2} [4 ln (x + 1) + ln (x) - ln (x^{4} - 3)]

ln (\frac{6}{x ^{2} + 1})

\frac{1}{2} ln (x) - ln (9)

lo g_{x} (\frac{1}{81})

3 (ln (ln (4)) - ln (ln (2)))

What is log_{9}(6)+1/2*log_{9}(a)+1/2*log_{9}(b) ?
The solution to log_{9}(6)+1/2*log_{9}(a)+1/2*log_{9}(b) is log_{9}(6a^{1/2}b^{1/2})