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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

8 lo g_{10} (b) = lo g_{10} (b^{8})

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

Apply log rule:

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

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

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

ln (\frac{27 - 10}{9.9 - 10})

ln \frac{x + y}{x + x \cdot ( 1 + \frac{y}{x} ) ^{\frac{1}{2}} - x}

\frac{7 2}{8} - \frac{5 2}{4} ln (22)

- ln (x + 1) - ln (x)

ln (a^{5} b^{4})

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