What is ln(x^{10}sqrt(5-x)) ?

The solution to ln(x^{10}sqrt(5-x)) is 10ln(x)+ln(sqrt(5-x))

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simplify ln(x^{10}sqrt(5-x))

simplify

ln (x^{10} 5 - x)

10 ln (x) + ln (5 - x)

Solution steps

ln (x^{10} 5 - x)

Apply log rule:

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

ln (x^{10} 5 - x) = ln (x^{10}) + ln (5 - x)

= ln (x^{10}) + ln (- x + 5)

Apply log rule:

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

ln (x^{10}) = 10 ln (x)

= 10 ln (x) + ln (5 - x)

lo g_{7} (8 yz)

lo g_{11} (\frac{11}{y})

3.13 + lo g_{10} (\frac{[ 0.5 ]}{[ 0.3 ]})

lo g_{10} (10 x^{2})

4 lo g_{2} (x) - \frac{1}{3} lo g_{2} (x^{2} + 1)

What is ln(x^{10}sqrt(5-x)) ?
The solution to ln(x^{10}sqrt(5-x)) is 10ln(x)+ln(sqrt(5-x))