What is ln((5a)/(2b^3)) ?

The solution to ln((5a)/(2b^3)) is ln(5)+ln(a)-ln(2)-3ln(b)

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simplify ln((5a)/(2b^3))

simplify

ln (\frac{5 a}{2 b ^{3}})

ln (5) + ln (a) - ln (2) - 3 ln (b)

Solution steps

ln (\frac{5 a}{2 b ^{3}})

Apply log rule:

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

ln (\frac{5 a}{2 b ^{3}}) = ln (5 a) - ln (2 b^{3})

= ln (5 a) - ln (2 b^{3})

Apply log rule:

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

ln (5 a) = ln (5) + ln (a), ln (2 b^{3}) = ln (2) + ln (b^{3})

= ln (5) + ln (a) - (ln (b^{3}) + ln (2))

Apply log rule:

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

ln (b^{3}) = 3 ln (b)

= ln (5) + ln (a) - (ln (2) + 3 ln (b))

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

= ln (5) + ln (a) - ln (2) - 3 ln (b)

ln (\frac{78}{90})

ln (\frac{5}{x + 1})

f (x) = ln (x) + ln (25)

ln (5) \cdot 3

ln (\frac{1}{2}) - ln (x)

What is ln((5a)/(2b^3)) ?
The solution to ln((5a)/(2b^3)) is ln(5)+ln(a)-ln(2)-3ln(b)