What is ln((2x^4)/(y^7)) ?

The solution to ln((2x^4)/(y^7)) is ln(2)+4ln(x)-7ln(y)

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simplify ln((2x^4)/(y^7))

simplify

ln (\frac{2 x ^{4}}{y ^{7}})

ln (2) + 4 ln (x) - 7 ln (y)

Solution steps

ln (\frac{2 x ^{4}}{y ^{7}})

Apply log rule:

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

ln (\frac{2 x ^{4}}{y ^{7}}) = ln (2 x^{4}) - ln (y^{7})

= ln (2 x^{4}) - ln (y^{7})

Apply log rule:

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

ln (y^{7}) = 7 ln (y)

= ln (2 x^{4}) - 7 ln (y)

Apply log rule:

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

ln (2 x^{4}) = ln (2) + ln (x^{4})

= ln (2) + ln (x^{4}) - 7 ln (y)

Apply log rule:

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

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

= ln (2) + 4 ln (x) - 7 ln (y)

ln (\frac{0.525}{0.412})

- lo g_{10} (2.17 \cdot 1 0^{- 9})

ln (7) - ln (14) + ln (10)

ln (x + 3) + 2 ln (y) - ln (a) + ln (b)

- lo g_{10} (8 \cdot 1 0^{- 6})

What is ln((2x^4)/(y^7)) ?
The solution to ln((2x^4)/(y^7)) is ln(2)+4ln(x)-7ln(y)