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Popular >

simplify ln(2x)-ln(6x)+ln(3x)

Solution

simplify

ln (2 x) - ln (6 x) + ln (3 x)

Solution

ln (x)

Solution steps

ln (2 x) - ln (6 x) + ln (3 x)

Apply log rule:

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

ln (2 x) - ln (6 x) = ln (\frac{2 x}{6 x})

= ln (\frac{2 x}{6 x}) + ln (3 x)

\frac{2 x}{6 x} = \frac{1}{3}

= ln (\frac{1}{3}) + ln (3 x)

Apply log rule:

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

ln (\frac{1}{3}) + ln (3 x) = ln (3 \cdot \frac{1}{3} x)

= ln (3 \cdot \frac{1}{3} x)

Simplify

\frac{1}{3} \cdot 3 x : x

= ln (x)

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Frequently Asked Questions (FAQ)

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