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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 lo g_{10} (b) - \frac{1}{2} (lo g_{10} (c) + 4 lo g_{10} (d)) + 5 lo g_{10} (h)

3 ln (10) - 4 ln (2) - ln (5)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

lo g_{b} (\frac{x ^{2} y}{z ^{2}})

ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}})

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