What is 1/2 log_{10}(a)+6log_{10}(b) ?

The solution to 1/2 log_{10}(a)+6log_{10}(b) is log_{10}(a^{1/2}b^6)

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simplify 1/2 log_{10}(a)+6log_{10}(b)

simplify

\frac{1}{2} lo g_{10} (a) + 6 lo g_{10} (b)

lo g_{10} (a^{\frac{1}{2}} b^{6})

Solution steps

\frac{1}{2} lo g_{10} (a) + 6 lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{\frac{1}{2}}) + 6 lo g_{10} (b)

Apply log rule:

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

6 lo g_{10} (b) = lo g_{10} (b^{6})

= lo g_{10} (a^{\frac{1}{2}}) + lo g_{10} (b^{6})

Apply log rule:

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

lo g_{10} (a^{\frac{1}{2}}) + lo g_{10} (b^{6}) = lo g_{10} (b^{6} a^{\frac{1}{2}})

= lo g_{10} (a^{\frac{1}{2}} b^{6})

8 ln (x) - \frac{1}{7} ln (y)

- \frac{4}{10} lo g_{2} (\frac{4}{10}) - \frac{6}{10} lo g_{2} (\frac{6}{10})

ln (\frac{3 x - 5}{7})

lo g_{49} (\frac{20000}{50}) + 1

lo g_{10} (\frac{7 ( x + 6 ) ^{3}}{x ^{5}})

What is 1/2 log_{10}(a)+6log_{10}(b) ?
The solution to 1/2 log_{10}(a)+6log_{10}(b) is log_{10}(a^{1/2}b^6)