What is ln((a^2b^4)/(c^8)) ?

The solution to ln((a^2b^4)/(c^8)) is 2ln(a)+4ln(b)-8ln(c)

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simplify ln((a^2b^4)/(c^8))

simplify

ln (\frac{a ^{2} b ^{4}}{c ^{8}})

2 ln (a) + 4 ln (b) - 8 ln (c)

Solution steps

ln (\frac{a ^{2} b ^{4}}{c ^{8}})

Apply log rule:

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

ln (\frac{a ^{2} b ^{4}}{c ^{8}}) = ln (a^{2} b^{4}) - ln (c^{8})

= ln (a^{2} b^{4}) - ln (c^{8})

Apply log rule:

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

ln (c^{8}) = 8 ln (c)

= ln (a^{2} b^{4}) - 8 ln (c)

Apply log rule:

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

ln (a^{2} b^{4}) = ln (a^{2}) + ln (b^{4})

= ln (a^{2}) + ln (b^{4}) - 8 ln (c)

Apply log rule:

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

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

= 2 ln (a) + ln (b^{4}) - 8 ln (c)

Apply log rule:

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

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

= 2 ln (a) + 4 ln (b) - 8 ln (c)

ln (\frac{47}{50}) + (0.085)

ln (\frac{( x + 2 ) ^{7}}{x ^{5}})

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t)

- lo g_{10} (1.8 \cdot 10)

0.026 ln (5 \cdot 1 0^{12 - 4})

What is ln((a^2b^4)/(c^8)) ?
The solution to ln((a^2b^4)/(c^8)) is 2ln(a)+4ln(b)-8ln(c)