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Popular >

simplify ln((3x^5)/y)

Solution

simplify

ln (\frac{3 x ^{5}}{y})

Solution

ln (3) + 5 ln (x) - ln (y)

Solution steps

ln (\frac{3 x ^{5}}{y})

Apply log rule:

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

ln (\frac{3 x ^{5}}{y}) = ln (3 x^{5}) - ln (y)

= ln (3 x^{5}) - ln (y)

Apply log rule:

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

ln (3 x^{5}) = ln (3) + ln (x^{5})

= ln (3) + ln (x^{5}) - ln (y)

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= ln (3) + 5 ln (x) - ln (y)

Popular Examples

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join sqrt(3)*ln(5)join

3 \cdot ln (5)

Frequently Asked Questions (FAQ)

What is ln((3x^5)/y) ?
The solution to ln((3x^5)/y) is ln(3)+5ln(x)-ln(y)