What is ln((a^1)/(b^3c^4)) ?

The solution to ln((a^1)/(b^3c^4)) is ln(a)-3ln(b)-4ln(c)

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simplify ln((a^1)/(b^3c^4))

simplify

ln (\frac{a ^{1}}{b ^{3} c ^{4}})

ln (a) - 3 ln (b) - 4 ln (c)

Solution steps

ln (\frac{a ^{1}}{b ^{3} c ^{4}})

Apply log rule:

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

ln (\frac{a ^{1}}{b ^{3} c ^{4}}) = ln (a^{1}) - ln (b^{3} c^{4})

= ln (a^{1}) - ln (b^{3} c^{4})

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} c^{4})

Apply log rule:

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

ln (b^{3} c^{4}) = ln (b^{3}) + ln (c^{4})

= 1 \cdot ln (a) - (ln (b^{3}) + ln (c^{4}))

Apply log rule:

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

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

= 1 \cdot ln (a) - (3 ln (b) + ln (c^{4}))

Apply log rule:

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

ln (c^{4}) = 4 ln (c)

= 1 \cdot ln (a) - (3 ln (b) + 4 ln (c))

Multiply:

1 \cdot ln (a) = ln (a)

= ln (a) - (3 ln (b) + 4 ln (c))

- (3 ln (b) + 4 ln (c)) : - 3 ln (b) - 4 ln (c)

= ln (a) - 3 ln (b) - 4 ln (c)

x^{4} - ln (x y) + 3^{2 x + y^{2}}

lo g_{4} (n) + 3 lo g_{4} (m)

- lo g_{10} (8.2 \cdot 1 0^{- 5})

- ln (\frac{2}{cos ( x )})

lo g_{10} (6 x^{4})

What is ln((a^1)/(b^3c^4)) ?
The solution to ln((a^1)/(b^3c^4)) is ln(a)-3ln(b)-4ln(c)