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)

lo g_{10} (2) + lo g_{10} (4) - lo g_{10} (7)

lo g_{3} (\frac{x ^{8} y ^{4}}{6})

ln (x^{13} 2 - x)

f (x) = lo g_{10} (x - 2) + lo g_{10} (x) - lo g_{10} (8)

lo g_{10} (z x^{8})

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)