What is 5log_{3}(a)+log_{3}(b-1) ?

The solution to 5log_{3}(a)+log_{3}(b-1) is log_{3}(a^5(b-1))

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simplify 5log_{3}(a)+log_{3}(b-1)

simplify

5 lo g_{3} (a) + lo g_{3} (b - 1)

lo g_{3} (a^{5} (b - 1))

Solution steps

5 lo g_{3} (a) + lo g_{3} (b - 1)

Apply log rule:

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

5 lo g_{3} (a) = lo g_{3} (a^{5})

= lo g_{3} (a^{5}) + lo g_{3} (b - 1)

Apply log rule:

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

lo g_{3} (a^{5}) + lo g_{3} (b - 1) = lo g_{3} (a^{5} (b - 1))

= lo g_{3} (a^{5} (b - 1))

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

ln (\frac{2 x - 3}{x + 1})

lo g_{3} (x) - lo g_{3} (x^{7})

- \frac{1}{20} ln (\frac{1}{2})

What is 5log_{3}(a)+log_{3}(b-1) ?
The solution to 5log_{3}(a)+log_{3}(b-1) is log_{3}(a^5(b-1))