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Popular >

simplify ln((x^3y^4)/z)

Solution

simplify

ln (\frac{x ^{3} y ^{4}}{z})

Solution

3 ln (x) + 4 ln (y) - ln (z)

Solution steps

ln (\frac{x ^{3} y ^{4}}{z})

Apply log rule:

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

ln (\frac{x ^{3} y ^{4}}{z}) = ln (x^{3} y^{4}) - ln (z)

= ln (x^{3} y^{4}) - ln (z)

Apply log rule:

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

ln (x^{3} y^{4}) = ln (x^{3}) + ln (y^{4})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 ln (x) + 4 ln (y) - ln (z)

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Frequently Asked Questions (FAQ)

What is ln((x^3y^4)/z) ?
The solution to ln((x^3y^4)/z) is 3ln(x)+4ln(y)-ln(z)