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Popular >

simplify ln(e/(x^2y^3z))

Solution

simplify

ln (\frac{e}{x ^{2} y ^{3} z})

Solution

1 - 2 ln (x) - 3 ln (y) - ln (z)

Solution steps

ln (\frac{e}{x ^{2} y ^{3} z})

Apply log rule:

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

ln (\frac{e}{x ^{2} y ^{3} z}) = ln (e) - ln (x^{2} y^{3} z)

= ln (e) - ln (x^{2} y^{3} z)

Apply log rule:

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

ln (x^{2} y^{3} z) = ln (x^{2}) + ln (y^{3}) + ln (z)

= ln (e) - (ln (x^{2}) + ln (y^{3}) + ln (z))

Apply log rule:

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

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

= ln (e) - (2 ln (x) + ln (y^{3}) + ln (z))

Apply log rule:

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

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

= ln (e) - (2 ln (x) + 3 ln (y) + ln (z))

Apply log rule:

lo g_{a} (a) = 1

= 1 - (2 ln (x) + 3 ln (y) + ln (z))

- (2 ln (x) + 3 ln (y) + ln (z)) : - 2 ln (x) - 3 ln (y) - ln (z)

= 1 - 2 ln (x) - 3 ln (y) - ln (z)

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Frequently Asked Questions (FAQ)

What is ln(e/(x^2y^3z)) ?
The solution to ln(e/(x^2y^3z)) is 1-2ln(x)-3ln(y)-ln(z)