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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

lo g_{7} (2 \cdot 6) + lo g_{7} (3)

- \frac{1}{14} ln ∣ 3 x - 1 ∣ - 3 ln ∣ 3 - 2 ∣ + \frac{32}{7} ln ∣ 3 + 3 ∣

lo g_{b} (z^{6} x)

\frac{2 ln ( 3 )}{ln ( 7 )} + 6

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