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Popular >

simplify ln((e^{xln(3)})/3)

Solution

simplify

ln (\frac{e ^{x l n (3)}}{3})

Solution

ln (3) x - ln (3)

Solution steps

ln (\frac{e ^{x l n (3)}}{3})

Apply log rule:

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

ln (\frac{e ^{x l n (3)}}{3}) = ln (e^{x l n (3)}) - ln (3)

= ln (e^{l n (3) x}) - ln (3)

Apply log rule:

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

ln (e^{x l n (3)}) = x ln (3) ln (e)

= x ln (3) ln (e) - ln (3)

x ln (3) ln (e) = ln (3) x

= ln (3) x - ln (3)

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Frequently Asked Questions (FAQ)

What is ln((e^{xln(3)})/3) ?
The solution to ln((e^{xln(3)})/3) is ln(3)x-ln(3)