What is log_{3}(9x^4)-log_{3}((3x)^2) ?

The solution to log_{3}(9x^4)-log_{3}((3x)^2) is 2log_{3}(x)

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simplify log_{3}(9x^4)-log_{3}((3x)^2)

simplify

lo g_{3} (9 x^{4}) - lo g_{3} ((3 x)^{2})

2 lo g_{3} (x)

Solution steps

lo g_{3} (9 x^{4}) - lo g_{3} ((3 x)^{2})

Apply log rule:

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

lo g_{3} (9 x^{4}) - lo g_{3} ((3 x)^{2}) = lo g_{3} (\frac{9 x ^{4}}{( 3 x ) ^{2}})

= lo g_{3} (\frac{9 x ^{4}}{( 3 x ) ^{2}})

Cancel

\frac{9 x ^{4}}{( 3 x ) ^{2}} : x^{2}

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 2 lo g_{3} (x)

ln (2 arccot (x))

ln (\frac{e ^{3}}{7})

\frac{2 ln ( 3 ) - 4 ln ( 5 )}{7 ln ( 5 ) - ln ( 3 )}

lo g_{10} (\frac{x}{10 y ^{5}})

What is log_{3}(9x^4)-log_{3}((3x)^2) ?
The solution to log_{3}(9x^4)-log_{3}((3x)^2) is 2log_{3}(x)