What is ln(x^{15}sqrt(2-x)) ?

The solution to ln(x^{15}sqrt(2-x)) is 15ln(x)+ln(sqrt(2-x))

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simplify ln(x^{15}sqrt(2-x))

simplify

ln (x^{15} 2 - x)

15 ln (x) + ln (2 - x)

Solution steps

ln (x^{15} 2 - x)

Apply log rule:

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

ln (x^{15} 2 - x) = ln (x^{15}) + ln (2 - x)

= ln (x^{15}) + ln (- x + 2)

Apply log rule:

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

ln (x^{15}) = 15 ln (x)

= 15 ln (x) + ln (2 - x)

ln (\frac{5 ^{2}}{5 ^{2} + ( - 5 ) ^{2}})

\frac{2}{3} lo g_{8} (7) - lo g_{8} (5)

(\frac{1}{e})^{2} lo g_{7} (\frac{1}{e})

ln (\frac{r}{4 s})

0.4 \cdot lo g_{2} (0.4) + 0.6 \cdot lo g_{2} (0.6)

What is ln(x^{15}sqrt(2-x)) ?
The solution to ln(x^{15}sqrt(2-x)) is 15ln(x)+ln(sqrt(2-x))