What is ln(((a^3b^5))/(6sqrt(c))) ?

The solution to ln(((a^3b^5))/(6sqrt(c))) is 3ln(a)+5ln(b)-ln(6)-ln(sqrt(c))

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simplify ln(((a^3b^5))/(6sqrt(c)))

simplify

ln (\frac{( a ^{3} b ^{5} )}{6 c})

3 ln (a) + 5 ln (b) - ln (6) - ln (c)

Solution steps

ln (\frac{( a ^{3} b ^{5} )}{6 c})

Apply log rule:

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

ln (\frac{( a ^{3} b ^{5} )}{6 c}) = ln ((a^{3} b^{5})) - ln (6 c)

= ln (a^{3} b^{5}) - ln (6 c)

Apply log rule:

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

ln (a^{3} b^{5}) = ln (a^{3}) + ln (b^{5}), ln (6 c) = ln (6) + ln (c)

= ln (a^{3}) + ln (b^{5}) - (ln (c) + ln (6))

Apply log rule:

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

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

= 3 ln (a) + ln (b^{5}) - (ln (6) + ln (c))

Apply log rule:

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

ln (b^{5}) = 5 ln (b)

= 3 ln (a) + 5 ln (b) - (ln (6) + ln (c))

- (ln (6) + ln (c)) : - ln (6) - ln (c)

= 3 ln (a) + 5 ln (b) - ln (6) - ln (c)

lo g_{4} (x^{4}) y

5 ln (\frac{5}{2}) - 5

2 lo g_{10} (x + 3) - 5 lo g_{10} (x - 1)

ln (5 e^{- i \frac{7 π}{4}})

What is ln(((a^3b^5))/(6sqrt(c))) ?
The solution to ln(((a^3b^5))/(6sqrt(c))) is 3ln(a)+5ln(b)-ln(6)-ln(sqrt(c))