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Popular >

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

Solution

simplify

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

Solution

2 ln (y) - 2 ln (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify-log_{10}(4.907*10^{-3})simplify

- lo g_{10} (4.907 \cdot 1 0^{- 3})

simplify ln(a/(b+c))simplify

ln (\frac{a}{b + c})

simplify-log_{10}(1.6*10^{-11})simplify

- lo g_{10} (1.6 \cdot 1 0^{- 11})

simplify log_{e}((e^{-y}y^x)/(x!))simplify

lo g_{e} (\frac{e ^{- y} y ^{x}}{x !})

simplify 0.4*log_{10}(1/(0.4))+(1-0.4)*log_{10}(1/(1-0.4))simplify

0.4 \cdot lo g_{10} (\frac{1}{0.4}) + (1 - 0.4) \cdot lo g_{10} (\frac{1}{1 - 0.4})

Frequently Asked Questions (FAQ)

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