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Popular >

simplify ln(x^3e^{2x-1})

Solution

simplify

ln (x^{3} e^{2 x - 1})

Solution

3 ln (x) + 2 x - 1

Solution steps

ln (x^{3} e^{2 x - 1})

Apply log rule:

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

ln (x^{3} e^{2 x - 1}) = ln (x^{3}) + ln (e^{2 x - 1})

= ln (x^{3}) + ln (e^{2 x - 1})

Apply log rule:

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

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

= 3 ln (x) + ln (e^{2 x - 1})

Apply log rule:

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

ln (e^{2 x - 1}) = (2 x - 1) ln (e)

= 3 ln (x) + (2 x - 1) ln (e)

(2 x - 1) ln (e) = 2 x - 1

= 3 ln (x) + 2 x - 1

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Frequently Asked Questions (FAQ)

What is ln(x^3e^{2x-1}) ?
The solution to ln(x^3e^{2x-1}) is 3ln(x)+2x-1