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Popular >

simplify ln(2x^{8/(1-x)})

Solution

simplify

ln (2 x^{\frac{8}{1 - x}})

Solution

ln (2) + \frac{8 ln ( x )}{1 - x}

Solution steps

ln (2 x^{\frac{8}{1 - x}})

Apply log rule:

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

ln (2 x^{\frac{8}{1 - x}}) = ln (2) + ln (x^{\frac{8}{1 - x}})

= ln (2) + ln (x^{\frac{8}{- x + 1}})

Apply log rule:

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

ln (x^{\frac{8}{1 - x}}) = \frac{8}{1 - x} ln (x)

= ln (2) + \frac{8}{1 - x} ln (x)

Multiply

\frac{8}{1 - x} ln (x) : \frac{8 ln ( x )}{1 - x}

= ln (2) + \frac{8 ln ( x )}{- x + 1}

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Frequently Asked Questions (FAQ)

What is ln(2x^{8/(1-x)}) ?
The solution to ln(2x^{8/(1-x)}) is ln(2)+(8ln(x))/(1-x)