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Popular >

simplify ln(e^{4x}x^7)

Solution

simplify

ln (e^{4 x} x^{7})

Solution

4 x + 7 ln (x)

Solution steps

ln (e^{4 x} x^{7})

Apply log rule:

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

ln (e^{4 x} x^{7}) = ln (e^{4 x}) + ln (x^{7})

= ln (e^{4 x}) + ln (x^{7})

Apply log rule:

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

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

= 4 x ln (e) + ln (x^{7})

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 4 x ln (e) + 7 ln (x)

4 x ln (e) = 4 x

= 4 x + 7 ln (x)

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Frequently Asked Questions (FAQ)

What is ln(e^{4x}x^7) ?
The solution to ln(e^{4x}x^7) is 4x+7ln(x)