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Popular >

simplify ln((a^{25})/(a^3))

Solution

simplify

ln (\frac{a ^{25}}{a ^{3}})

Solution

22 ln (a)

Solution steps

ln (\frac{a ^{25}}{a ^{3}})

Apply log rule:

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

ln (\frac{a ^{25}}{a ^{3}}) = ln (a^{25}) - ln (a^{3})

= ln (a^{25}) - ln (a^{3})

Apply log rule:

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

ln (a^{25}) = 25 ln (a)

= 25 ln (a) - ln (a^{3})

Apply log rule:

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

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

= 25 ln (a) - 3 ln (a)

Add similar elements:

25 ln (a) - 3 ln (a) = 22 ln (a)

= 22 ln (a)

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Frequently Asked Questions (FAQ)

What is ln((a^{25})/(a^3)) ?
The solution to ln((a^{25})/(a^3)) is 22ln(a)