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Popular >

simplify ln(4/3 x^2)

Solution

simplify

ln (\frac{4}{3} x^{2})

Solution

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

Solution steps

ln (\frac{4}{3} x^{2})

Apply log rule:

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

ln (\frac{4}{3} x^{2}) = ln (\frac{4}{3}) + ln (x^{2})

= ln (\frac{4}{3}) + ln (x^{2})

Apply log rule:

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

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

= ln (\frac{4}{3}) + 2 ln (x)

Apply log rule:

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

ln (\frac{4}{3}) = ln (4) - ln (3)

= ln (4) - ln (3) + 2 ln (x)

ln (4) = 2 ln (2)

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

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Frequently Asked Questions (FAQ)

What is ln(4/3 x^2) ?
The solution to ln(4/3 x^2) is 2ln(2)-ln(3)+2ln(x)