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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

4 lo g_{10} (b) = lo g_{10} (b^{4})

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

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

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

2 lo g_{a} (x) - lo g_{a} (x - 1) - lo g_{a} (x - 2)

ln (\frac{r}{8 s})

lo g_{10} (6) + 2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{6} ((3 \cdot 11)^{6})

\frac{4 ln ( \frac{54}{7} )}{ln ( 2 )}

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