What is ln(4a^{(3)}b^{(5)}) ?

The solution to ln(4a^{(3)}b^{(5)}) is 2ln(2)+3ln(a)+5ln(b)

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simplify ln(4a^{(3)}b^{(5)})

simplify

ln (4 a^{(3)} b^{(5)})

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

Solution steps

ln (4 a^{(3)} b^{(5)})

Apply log rule:

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

ln (4 a^{(3)} b^{(5)}) = ln (4) + ln (a^{(3)}) + ln (b^{(5)})

= ln (4) + ln (a^{(3)}) + ln (b^{(5)})

Apply log rule:

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

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

= ln (4) + 3 ln (a) + ln (b^{5})

Apply log rule:

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

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

= ln (4) + 3 ln (a) + 5 ln (b)

ln (4) = 2 ln (2)

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

4 lo g_{10} (x + 6) - lo g_{10} (x)

ln (\frac{4 x}{2 + x ^{2}})

- lo g_{10} (1.07 \cdot 1 0^{- 6})

- lo g_{10} (1.47 x 1 0^{- 150})

ln (\frac{x}{14})

What is ln(4a^{(3)}b^{(5)}) ?
The solution to ln(4a^{(3)}b^{(5)}) is 2ln(2)+3ln(a)+5ln(b)