What is 1/2 log_{10}(b)+3log_{10}(c) ?

The solution to 1/2 log_{10}(b)+3log_{10}(c) is log_{10}(b^{1/2}c^3)

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simplify 1/2 log_{10}(b)+3log_{10}(c)

simplify

\frac{1}{2} lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{10} (b^{\frac{1}{2}} c^{3})

Solution steps

\frac{1}{2} lo g_{10} (b) + 3 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}}) + 3 lo g_{10} (c)

Apply log rule:

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

3 lo g_{10} (c) = lo g_{10} (c^{3})

= lo g_{10} (b^{\frac{1}{2}}) + lo g_{10} (c^{3})

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^{3}) = lo g_{10} (c^{3} b^{\frac{1}{2}})

= lo g_{10} (b^{\frac{1}{2}} c^{3})

- lo g_{2} (\frac{x}{3})

4 ln (x) - 6 ln (y)

3 + lo g_{10} (\frac{x}{10})

lo g_{3} (\frac{27}{x})

lo g_{10} (\frac{y ^{4}}{100 x})

What is 1/2 log_{10}(b)+3log_{10}(c) ?
The solution to 1/2 log_{10}(b)+3log_{10}(c) is log_{10}(b^{1/2}c^3)