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Popular >

simplify ln((5x)/(y^2))

Solution

simplify

ln (\frac{5 x}{y ^{2}})

Solution

ln (5) + ln (x) - 2 ln (y)

Solution steps

ln (\frac{5 x}{y ^{2}})

Apply log rule:

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

ln (\frac{5 x}{y ^{2}}) = ln (5 x) - ln (y^{2})

= ln (5 x) - ln (y^{2})

Apply log rule:

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

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

= ln (5 x) - 2 ln (y)

Apply log rule:

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

ln (5 x) = ln (5) + ln (x)

= ln (5) + ln (x) - 2 ln (y)

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Frequently Asked Questions (FAQ)

What is ln((5x)/(y^2)) ?
The solution to ln((5x)/(y^2)) is ln(5)+ln(x)-2ln(y)