What is log_{x}(18a^5)-2log_{x}(3a) ?

The solution to log_{x}(18a^5)-2log_{x}(3a) is log_{x}(2a^3)

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simplify log_{x}(18a^5)-2log_{x}(3a)

simplify

lo g_{x} (18 a^{5}) - 2 lo g_{x} (3 a)

lo g_{x} (2 a^{3})

Solution steps

lo g_{x} (18 a^{5}) - 2 lo g_{x} (3 a)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 2 lo g_{x} (3 a) = - lo g_{x} ((3 a)^{2})

= lo g_{x} (18 a^{5}) - lo g_{x} ((3 a)^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{x} (18 a^{5}) - lo g_{x} ((3 a)^{2}) = lo g_{x} (\frac{18 a ^{5}}{( 3 a ) ^{2}})

= lo g_{x} (\frac{18 a ^{5}}{( 3 a ) ^{2}})

Cancel

\frac{18 a ^{5}}{( 3 a ) ^{2}} : 2 a^{3}

= lo g_{x} (2 a^{3})

lo g_{3} (81 x^{3} 1 + x^{2})

lo g_{4} (x y^{4} z^{4})

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

lo g_{6} (60) - lo g_{6} (30)

lo g_{b} (u^{2} v^{9})

What is log_{x}(18a^5)-2log_{x}(3a) ?
The solution to log_{x}(18a^5)-2log_{x}(3a) is log_{x}(2a^3)