What is join 1/2 ln(1+(2y)/x) ?

The solution to join 1/2 ln(1+(2y)/x) is ln(((x+2y)/x)^{1/2})

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join 1/2 ln(1+(2y)/x)

join

\frac{1}{2} ln (1 + \frac{2 y}{x})

ln ((\frac{x + 2 y}{x})^{\frac{1}{2}})

Solution steps

\frac{1}{2} ln (1 + \frac{2 y}{x})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

(1 + \frac{2 y}{x})^{\frac{1}{2}} = (\frac{x + 2 y}{x})^{\frac{1}{2}}

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

ln (\frac{- 130.42}{- 0.00222877})

ln (x (60 - y))

ln (2 \cdot 3^{2 + 2 x})

\frac{2 ln ( 5 ) - 10 ln ( 9 )}{7 ln ( 5 ) - 2 ln ( 9 )}

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