What is ln((b^2asqrt(a))/c) ?

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

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simplify ln((b^2asqrt(a))/c)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{1.06} (5) - lo g_{1.06} (3)

ln (3^{3} 4 - x)

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

2 ln (x^{3} \cdot y \frac{1}{2})

ln (\frac{0.19556}{0.1563})

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