What is 6log_{10}(a)+log_{10}(b) ?

The solution to 6log_{10}(a)+log_{10}(b) is log_{10}(a^6b)

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simplify 6log_{10}(a)+log_{10}(b)

simplify

6 lo g_{10} (a) + lo g_{10} (b)

lo g_{10} (a^{6} b)

Solution steps

6 lo g_{10} (a) + lo g_{10} (b)

Apply log rule:

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

6 lo g_{10} (a) = lo g_{10} (a^{6})

= lo g_{10} (a^{6}) + lo g_{10} (b)

Apply log rule:

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

lo g_{10} (a^{6}) + lo g_{10} (b) = lo g_{10} (a^{6} b)

= lo g_{10} (a^{6} b)

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

\frac{1}{2} ln (x) + 5 ln (y) - 2 ln (z)

\frac{1}{2} lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (x)

lo g_{10} (a b^{3})

What is 6log_{10}(a)+log_{10}(b) ?
The solution to 6log_{10}(a)+log_{10}(b) is log_{10}(a^6b)