What is log_{3}(x)+log_{3}(6x)-log_{3}(x^2) ?

The solution to log_{3}(x)+log_{3}(6x)-log_{3}(x^2) is log_{3}(6)

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simplify log_{3}(x)+log_{3}(6x)-log_{3}(x^2)

simplify

lo g_{3} (x) + lo g_{3} (6 x) - lo g_{3} (x^{2})

lo g_{3} (6)

Decimal Notation

1.63092 \dots

Solution steps

lo g_{3} (x) + lo g_{3} (6 x) - lo g_{3} (x^{2})

Apply log rule:

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

lo g_{3} (x) + lo g_{3} (6 x) = lo g_{3} (6 xx)

= lo g_{3} (6 xx) - lo g_{3} (x^{2})

Simplify

x \cdot 6 x : 6 x^{2}

= lo g_{3} (6 x^{2}) - lo g_{3} (x^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{3} (6 x^{2}) - lo g_{3} (x^{2}) = lo g_{3} (\frac{6 x ^{2}}{x ^{2}})

= lo g_{3} (\frac{6 x ^{2}}{x ^{2}})

Cancel the common factor:

x^{2}

= lo g_{3} (6)

lo g_{10} (x + 5) + lo g_{10} (x + 1)

6 lo g_{9} (z) + \frac{1}{2} \cdot lo g_{9} (x)

ln (\frac{v}{t})

\frac{ln ( 66 ) \cdot ln ( 780 )}{ln ( 117.34 ) - ln ( 780 )}

- 0.287 ln (\frac{600}{90})

What is log_{3}(x)+log_{3}(6x)-log_{3}(x^2) ?
The solution to log_{3}(x)+log_{3}(6x)-log_{3}(x^2) is log_{3}(6)