What is ln(200(12/23)^{1/3}) ?

The solution to ln(200(12/23)^{1/3}) is ln(200)+1/3 (ln(12)-ln(23))

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simplify ln(200(12/23)^{1/3})

simplify

ln (200 (\frac{12}{23})^{\frac{1}{3}})

ln (200) + \frac{1}{3} (ln (12) - ln (23))

Decimal Notation

5.08145 \dots

Solution steps

ln (200 (\frac{12}{23})^{\frac{1}{3}})

Apply log rule:

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

ln (200 (\frac{12}{23})^{\frac{1}{3}}) = ln (200) + ln ((\frac{12}{23})^{\frac{1}{3}})

= ln (200) + ln ((\frac{12}{23})^{\frac{1}{3}})

Apply log rule:

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

ln ((\frac{12}{23})^{\frac{1}{3}}) = \frac{1}{3} ln (\frac{12}{23})

= ln (200) + \frac{1}{3} ln (\frac{12}{23})

Apply log rule:

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

ln (\frac{12}{23}) = ln (12) - ln (23)

= ln (200) + \frac{1}{3} (ln (12) - ln (23))

ln (\frac{9 x ^{2} - 6 y ^{2} - 36}{36})

2 x + ln (\frac{x ^{6}}{( x ^{2} - 2 x - 1 )})

lo g_{a} (\frac{x - x ^{\frac{1}{2}}}{( x - y ) ^{3}})

lo g_{2} (\frac{2 ( 3 x + 4 ) ^{2}}{2 ^{5} ( x + 1 ) ^{2}})

What is ln(200(12/23)^{1/3}) ?
The solution to ln(200(12/23)^{1/3}) is ln(200)+1/3 (ln(12)-ln(23))