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

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

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

join

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

- lo g_{10} (3.4 \cdot 1 0^{- 5})

\frac{ln ( 77 ) - 12 ln ( 2 )}{12 ln ( 2 )}

ln (\frac{1 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 3}})

lo g_{v} (b^{4}) (b^{9})

lo g_{6} ((\frac{u}{v ^{6}})^{5})

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