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Popular >

simplify ln(3^xe^{4x-1})

Solution

simplify

ln (3^{x} e^{4 x - 1})

Solution

ln (3) x + 4 x - 1

Solution steps

ln (3^{x} e^{4 x - 1})

Apply log rule:

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

ln (3^{x} e^{4 x - 1}) = ln (3^{x}) + ln (e^{4 x - 1})

= ln (3^{x}) + ln (e^{4 x - 1})

Apply log rule:

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

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

= x ln (3) + ln (e^{4 x - 1})

Apply log rule:

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

ln (e^{4 x - 1}) = (4 x - 1) ln (e)

= x ln (3) + (4 x - 1) ln (e)

(4 x - 1) ln (e) = 4 x - 1

= ln (3) x + 4 x - 1

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Frequently Asked Questions (FAQ)

What is ln(3^xe^{4x-1}) ?
The solution to ln(3^xe^{4x-1}) is ln(3)x+4x-1