What is 1/2 log_{10}(a)+9log_{10}(b) ?

The solution to 1/2 log_{10}(a)+9log_{10}(b) is log_{10}(a^{1/2}b^9)

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simplify 1/2 log_{10}(a)+9log_{10}(b)

simplify

\frac{1}{2} lo g_{10} (a) + 9 lo g_{10} (b)

lo g_{10} (a^{\frac{1}{2}} b^{9})

Solution steps

\frac{1}{2} lo g_{10} (a) + 9 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}}) + 9 lo g_{10} (b)

Apply log rule:

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

9 lo g_{10} (b) = lo g_{10} (b^{9})

= lo g_{10} (a^{\frac{1}{2}}) + lo g_{10} (b^{9})

Apply log rule:

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

lo g_{10} (a^{\frac{1}{2}}) + lo g_{10} (b^{9}) = lo g_{10} (b^{9} a^{\frac{1}{2}})

= lo g_{10} (a^{\frac{1}{2}} b^{9})

lo g_{10} (\frac{x}{1000 y ^{7}})

- \frac{1}{2} ln ∣ e^{y} ∣ + \frac{1}{2} ln ∣ e^{y} - 2 ∣

lo g_{10} (w^{6} u \cdot v)

lo g_{3} ((\frac{4 x}{y})^{2})

ln (x^{14} 6 - x)

What is 1/2 log_{10}(a)+9log_{10}(b) ?
The solution to 1/2 log_{10}(a)+9log_{10}(b) is log_{10}(a^{1/2}b^9)