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

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

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

simplify

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

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

Solution steps

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

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}})

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{10} (\frac{( 100 x ) ^{2}}{27})

3 [ln (x) - 2 ln (x^{2} + 1)] - 2 ln (5)

ln (\frac{x ^{2} y}{z ^{4}})

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

ln (21 e)

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