What is ln(sqrt(x-1)(2x-3)^{1/4}) ?

The solution to ln(sqrt(x-1)(2x-3)^{1/4}) is ln(sqrt(x-1))+1/4 ln(2x-3)

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simplify ln(sqrt(x-1)(2x-3)^{1/4})

simplify

ln (x - 1 (2 x - 3)^{\frac{1}{4}})

ln (x - 1) + \frac{1}{4} ln (2 x - 3)

Solution steps

ln (x - 1 (2 x - 3)^{\frac{1}{4}})

Apply log rule:

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

ln (x - 1 (2 x - 3)^{\frac{1}{4}}) = ln (x - 1) + ln ((2 x - 3)^{\frac{1}{4}})

= ln (x - 1) + ln ((2 x - 3)^{\frac{1}{4}})

Apply log rule:

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

ln ((2 x - 3)^{\frac{1}{4}}) = \frac{1}{4} ln (2 x - 3)

= ln (x - 1) + \frac{1}{4} ln (2 x - 3)

lo g_{b} (a^{5} b^{4})

lo g_{5} (100) + lo g_{5} (4)

ln (\frac{s ^{2} + 25}{s ^{2} + 81})

lo g_{a} (\frac{50}{9})

lo g_{10} (\frac{z ^{3}}{x})

What is ln(sqrt(x-1)(2x-3)^{1/4}) ?
The solution to ln(sqrt(x-1)(2x-3)^{1/4}) is ln(sqrt(x-1))+1/4 ln(2x-3)