What is ln(x^{12}sqrt(7-x)) ?

The solution to ln(x^{12}sqrt(7-x)) is 12ln(x)+ln(sqrt(7-x))

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simplify ln(x^{12}sqrt(7-x))

simplify

ln (x^{12} 7 - x)

12 ln (x) + ln (7 - x)

Solution steps

ln (x^{12} 7 - x)

Apply log rule:

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

ln (x^{12} 7 - x) = ln (x^{12}) + ln (7 - x)

= ln (x^{12}) + ln (- x + 7)

Apply log rule:

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

ln (x^{12}) = 12 ln (x)

= 12 ln (x) + ln (7 - x)

lo g_{10} (x) + lo g_{10} (x - 15)

ln (3 y)

lo g_{2} (\frac{8}{x - 1})

lo g_{8} (9) - lo g_{8} (11)

\frac{1}{- 0.032} ln (\frac{1}{2})

What is ln(x^{12}sqrt(7-x)) ?
The solution to ln(x^{12}sqrt(7-x)) is 12ln(x)+ln(sqrt(7-x))