What is 1/2 log_{10}(b)+4log_{10}(c) ?

The solution to 1/2 log_{10}(b)+4log_{10}(c) is log_{10}(b^{1/2}c^4)

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simplify 1/2 log_{10}(b)+4log_{10}(c)

simplify

\frac{1}{2} lo g_{10} (b) + 4 lo g_{10} (c)

lo g_{10} (b^{\frac{1}{2}} c^{4})

Solution steps

\frac{1}{2} lo g_{10} (b) + 4 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}}) + 4 lo g_{10} (c)

Apply log rule:

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

4 lo g_{10} (c) = lo g_{10} (c^{4})

= lo g_{10} (b^{\frac{1}{2}}) + lo g_{10} (c^{4})

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^{4}) = lo g_{10} (c^{4} b^{\frac{1}{2}})

= lo g_{10} (b^{\frac{1}{2}} c^{4})

ln (x + 1) - ln (x)

3 lo g_{5} (3 x + 1) - 2 lo g_{5} (2 x - 1) - lo g_{5} (x)

ln (x) + ln (18)

ln (a + b) + ln (a - b) - 4 ln (c)

lo g_{10} (\frac{5 y}{x ^{2}})

What is 1/2 log_{10}(b)+4log_{10}(c) ?
The solution to 1/2 log_{10}(b)+4log_{10}(c) is log_{10}(b^{1/2}c^4)