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Popular >

simplify ln((2x^2)/(3x))

Solution

simplify

ln (\frac{2 x ^{2}}{3 x})

Solution

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

Solution steps

ln (\frac{2 x ^{2}}{3 x})

Apply log rule:

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

ln (\frac{2 x ^{2}}{3 x}) = ln (2 x^{2}) - ln (3 x)

= ln (2 x^{2}) - ln (3 x)

Apply log rule:

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

ln (2 x^{2}) = ln (2) + ln (x^{2}), ln (3 x) = ln (3) + ln (x)

= ln (2) + ln (x^{2}) - (ln (x) + ln (3))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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