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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{10} (a) = lo g_{10} (a^{2})

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

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

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

Simplify

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

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

Apply log rule:

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

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

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

Simplify

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

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

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