What is 1/2 log_{10}(a)+5log_{10}(b) ?

The solution to 1/2 log_{10}(a)+5log_{10}(b) is log_{10}(a^{1/2}b^5)

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simplify 1/2 log_{10}(a)+5log_{10}(b)

simplify

\frac{1}{2} lo g_{10} (a) + 5 lo g_{10} (b)

lo g_{10} (a^{\frac{1}{2}} b^{5})

Solution steps

\frac{1}{2} lo g_{10} (a) + 5 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}}) + 5 lo g_{10} (b)

Apply log rule:

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

5 lo g_{10} (b) = lo g_{10} (b^{5})

= lo g_{10} (a^{\frac{1}{2}}) + lo g_{10} (b^{5})

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^{5}) = lo g_{10} (b^{5} a^{\frac{1}{2}})

= lo g_{10} (a^{\frac{1}{2}} b^{5})

lo g_{10} (7 x^{3} y)

lo g_{10} (\frac{y}{1000})

2 \cdot lo g_{4} (9) + 3 \cdot lo g_{4} (2)

lo g_{b} (z^{2} y)

3 lo g_{10} (4 x)

What is 1/2 log_{10}(a)+5log_{10}(b) ?
The solution to 1/2 log_{10}(a)+5log_{10}(b) is log_{10}(a^{1/2}b^5)