What is 2/7 log_{10}(a)-1/4 log_{10}(b) ?

The solution to 2/7 log_{10}(a)-1/4 log_{10}(b) is log_{10}((a^{2/7}b^{3/4})/b)

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simplify 2/7 log_{10}(a)-1/4 log_{10}(b)

simplify

\frac{2}{7} lo g_{10} (a) - \frac{1}{4} lo g_{10} (b)

lo g_{10} (\frac{a ^{\frac{2}{7}} b ^{\frac{3}{4}}}{b})

Solution steps

\frac{2}{7} lo g_{10} (a) - \frac{1}{4} lo g_{10} (b)

Apply log rule:

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

\frac{2}{7} lo g_{10} (a) = lo g_{10} (a^{\frac{2}{7}})

= lo g_{10} (a^{\frac{2}{7}}) - \frac{1}{4} lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{\frac{2}{7}}) - lo g_{10} (b^{\frac{1}{4}})

Apply log rule:

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

lo g_{10} (a^{\frac{2}{7}}) - lo g_{10} (b^{\frac{1}{4}}) = lo g_{10} (\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{4}}})

= lo g_{10} (\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{4}}})

Simplify

\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{4}}} : \frac{a ^{\frac{2}{7}} b ^{\frac{3}{4}}}{b}

= lo g_{10} (\frac{a ^{\frac{2}{7}} b ^{\frac{3}{4}}}{b})

- lo g_{10} (2.68 \cdot 1 0^{- 3})

ln (\frac{4 x ^{2} - x - 1}{3 x ^{2} + 5})

lo g_{10} (X^{6} Y)

\frac{1}{0.00003} ln (\frac{400 - 15}{75 - 15})

ln (4.98 \cdot 1 0^{15})

What is 2/7 log_{10}(a)-1/4 log_{10}(b) ?
The solution to 2/7 log_{10}(a)-1/4 log_{10}(b) is log_{10}((a^{2/7}b^{3/4})/b)