What is ln(A^1*sqrt(B^3)) ?

The solution to ln(A^1*sqrt(B^3)) is ln(A)+ln(sqrt(B)sqrt(B^2))

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simplify ln(A^1*sqrt(B^3))

simplify

ln (A^{1} \cdot B^{3})

ln (A) + ln (B B^{2})

Solution steps

ln (A^{1} B^{3})

Apply log rule:

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

ln (A^{1} B^{3}) = ln (A^{1}) + ln (B^{3})

= ln (A^{1}) + ln (B^{3})

Apply log rule:

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

ln (A^{1}) = 1 \cdot ln (A)

= 1 \cdot ln (A) + ln (B^{3})

Multiply:

1 \cdot ln (A) = ln (A)

= ln (A) + ln (B^{3})

B^{3} = B B^{2}

= ln (A) + ln (B B^{2})

\frac{1}{9} ln (x - 15) - \frac{1}{9} ln (x - 6)

t, s t + 1 = t^{2} + s

z^{2} = 4 + 4 r^{2}

(1 - 2 x) (1 - 3 x) = (5 x - 1) x - 2 (2 x - 5)

2 x^{2} + 16 x - 96 = 0

What is ln(A^1*sqrt(B^3)) ?
The solution to ln(A^1*sqrt(B^3)) is ln(A)+ln(sqrt(B)sqrt(B^2))