What is 1/2 log_{10}(b)+5log_{10}(c) ?

The solution to 1/2 log_{10}(b)+5log_{10}(c) is log_{10}(b^{1/2}c^5)

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simplify 1/2 log_{10}(b)+5log_{10}(c)

simplify

\frac{1}{2} lo g_{10} (b) + 5 lo g_{10} (c)

lo g_{10} (b^{\frac{1}{2}} c^{5})

Solution steps

\frac{1}{2} lo g_{10} (b) + 5 lo g_{10} (c)

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} (b^{\frac{1}{2}}) + 5 lo g_{10} (c)

Apply log rule:

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

5 lo g_{10} (c) = lo g_{10} (c^{5})

= lo g_{10} (b^{\frac{1}{2}}) + lo g_{10} (c^{5})

Apply log rule:

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

lo g_{10} (b^{\frac{1}{2}}) + lo g_{10} (c^{5}) = lo g_{10} (c^{5} b^{\frac{1}{2}})

= lo g_{10} (b^{\frac{1}{2}} c^{5})

ln (\frac{81162081}{390625})

lo g_{10} (\frac{6 x}{x + 2})

ln (\frac{5}{10})

lo g_{10} (\frac{x ^{2} y}{z})

lo g_{4} (7) - lo g_{4} (5)

What is 1/2 log_{10}(b)+5log_{10}(c) ?
The solution to 1/2 log_{10}(b)+5log_{10}(c) is log_{10}(b^{1/2}c^5)