What is 3log_{10}(a)+log_{10}(c) ?

The solution to 3log_{10}(a)+log_{10}(c) is log_{10}(a^3c)

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simplify 3log_{10}(a)+log_{10}(c)

simplify

3 lo g_{10} (a) + lo g_{10} (c)

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

Solution steps

3 lo g_{10} (a) + lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{3}) + lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a^{3}) + lo g_{10} (c) = lo g_{10} (a^{3} c)

= lo g_{10} (a^{3} c)

2 ln (8) - ln (4)

\frac{1}{2} (ln (6) - ln (4))

- 2 lo g_{10} (- 2 x) - 2

ln (\frac{30}{19.71})

ln (sec^{2} (x) cos^{3} (2 x))

What is 3log_{10}(a)+log_{10}(c) ?
The solution to 3log_{10}(a)+log_{10}(c) is log_{10}(a^3c)