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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (a^{3}) + lo g_{10} (b) = lo g_{10} (a^{3} b)

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Simplify

\frac{a ^{3} b}{c ^{\frac{1}{2}}} : \frac{a ^{3} b c}{c}

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

\frac{1}{5} lo g_{8} (3)

lo g_{10} (x^{3}) - lo g_{10} (y^{4}) + lo g_{10} (z)

ln (\frac{1 + 0.65}{365})

3 ln (2) + 2 ln (5)

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