What is 4log_{10}(a)+log_{10}(k) ?

The solution to 4log_{10}(a)+log_{10}(k) is log_{10}(a^4k)

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simplify 4log_{10}(a)+log_{10}(k)

simplify

4 lo g_{10} (a) + lo g_{10} (k)

lo g_{10} (a^{4} k)

Solution steps

4 lo g_{10} (a) + lo g_{10} (k)

Apply log rule:

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

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

= lo g_{10} (a^{4}) + lo g_{10} (k)

Apply log rule:

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

lo g_{10} (a^{4}) + lo g_{10} (k) = lo g_{10} (a^{4} k)

= lo g_{10} (a^{4} k)

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

2 lo g_{x} (4) + lo g_{x} (3)

lo g_{a} (\frac{x ^{7}}{y z ^{8}})

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

5 ln (cos^{2} (t)) + 5 ln (1 + tan^{2} (t))

What is 4log_{10}(a)+log_{10}(k) ?
The solution to 4log_{10}(a)+log_{10}(k) is log_{10}(a^4k)