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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

- lo g_{10} (4.5 \times 1 0^{- 4})

\frac{ln ( \frac{8}{9} )}{2 ln ( 6 )}

ln (x + 8) - ln (x - 8)

ln (e (x))

lo g_{10} (x^{2} + 2 x - 8) - lo g_{10} (x^{2} - 16)

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