What is 2/7 log_{10}(a)-1/8 log_{10}(b) ?

The solution to 2/7 log_{10}(a)-1/8 log_{10}(b) is log_{10}((a^{2/7}b^{7/8})/b)

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simplify 2/7 log_{10}(a)-1/8 log_{10}(b)

simplify

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} lo g_{10} (b)

lo g_{10} (\frac{a ^{\frac{2}{7}} b ^{\frac{7}{8}}}{b})

Solution steps

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} 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}{8} lo g_{10} (b)

Apply log rule:

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

\frac{1}{8} lo g_{10} (b) = lo g_{10} (b^{\frac{1}{8}})

= lo g_{10} (a^{\frac{2}{7}}) - lo g_{10} (b^{\frac{1}{8}})

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}{8}}) = lo g_{10} (\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{8}}})

= lo g_{10} (\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{8}}})

Simplify

\frac{a ^{\frac{2}{7}}}{b ^{\frac{1}{8}}} : \frac{a ^{\frac{2}{7}} b ^{\frac{7}{8}}}{b}

= lo g_{10} (\frac{a ^{\frac{2}{7}} b ^{\frac{7}{8}}}{b})

ln (ln (y)) + ln (x) + c

ln (\frac{432}{5})

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

ln (6.85 \cdot 1 0^{43})

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

What is 2/7 log_{10}(a)-1/8 log_{10}(b) ?
The solution to 2/7 log_{10}(a)-1/8 log_{10}(b) is log_{10}((a^{2/7}b^{7/8})/b)