What is 3/2 log_{10}(a)+5/2 log_{10}(b) ?

The solution to 3/2 log_{10}(a)+5/2 log_{10}(b) is log_{10}(a^{3/2}b^{5/2})

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simplify 3/2 log_{10}(a)+5/2 log_{10}(b)

simplify

\frac{3}{2} lo g_{10} (a) + \frac{5}{2} lo g_{10} (b)

lo g_{10} (a^{\frac{3}{2}} b^{\frac{5}{2}})

Solution steps

\frac{3}{2} lo g_{10} (a) + \frac{5}{2} lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{\frac{3}{2}}) + \frac{5}{2} lo g_{10} (b)

Apply log rule:

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

\frac{5}{2} lo g_{10} (b) = lo g_{10} (b^{\frac{5}{2}})

= lo g_{10} (a^{\frac{3}{2}}) + lo g_{10} (b^{\frac{5}{2}})

Apply log rule:

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

lo g_{10} (a^{\frac{3}{2}}) + lo g_{10} (b^{\frac{5}{2}}) = lo g_{10} (a^{\frac{3}{2}} b^{\frac{5}{2}})

= lo g_{10} (a^{\frac{3}{2}} b^{\frac{5}{2}})

lo g_{4} (k^{2} - 16) - lo g_{4} (k - 4)

ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{4 x}})

2 lo g_{2} (x) - 3 lo g_{2} (y)

21 lo g_{10} (x) - 5 lo g_{10} (q) + lo g_{10} (z^{2})

lo g_{10} (4) + lo g_{10} (8)

What is 3/2 log_{10}(a)+5/2 log_{10}(b) ?
The solution to 3/2 log_{10}(a)+5/2 log_{10}(b) is log_{10}(a^{3/2}b^{5/2})