What is simplify-ln(x)-ln(3)+ln(6) ?

The solution to simplify-ln(x)-ln(3)+ln(6) is ln(2/x)

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simplify-ln(x)-ln(3)+ln(6)

simplify

- ln (x) - ln (3) + ln (6)

ln (\frac{2}{x})

Solution steps

- ln (x) - ln (3) + ln (6)

Rewrite

- ln (x) - ln (3)

- (ln (x) + ln (3))

= - (ln (x) + ln (3)) + ln (6)

Apply log rule:

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

ln (x) + ln (3) = ln (3 x)

= - ln (x \cdot 3) + ln (6)

Apply log rule:

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

ln (6) - ln (3 x) = ln (\frac{6}{3 x})

= ln (\frac{6}{x \cdot 3})

Divide the numbers:

\frac{6}{3} = 2

= ln (\frac{2}{x})

0.5 lo g_{b} (x + 7) - lo g_{b} (x - 3)

- lo g_{10} (1.6 x 1 0^{- 4})

ln (y^{2} + 5) - ln (y^{2} - 2)

lo g_{6} (\frac{1}{120})

x + ln (x) + ln (2)

What is simplify-ln(x)-ln(3)+ln(6) ?
The solution to simplify-ln(x)-ln(3)+ln(6) is ln(2/x)