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Popular >

simplify ln((2x)/(y^{10)})

Solution

simplify

ln (\frac{2 x}{y ^{10}})

Solution

ln (2) + ln (x) - 10 ln (y)

Solution steps

ln (\frac{2 x}{y ^{10}})

Apply log rule:

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

ln (\frac{2 x}{y ^{10}}) = ln (2 x) - ln (y^{10})

= ln (2 x) - ln (y^{10})

Apply log rule:

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

ln (y^{10}) = 10 ln (y)

= ln (2 x) - 10 ln (y)

Apply log rule:

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

ln (2 x) = ln (2) + ln (x)

= ln (2) + ln (x) - 10 ln (y)

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Frequently Asked Questions (FAQ)

What is ln((2x)/(y^{10)}) ?
The solution to ln((2x)/(y^{10)}) is ln(2)+ln(x)-10ln(y)