What is 1/2 log_{10}(x+1)-2log_{10}(y-1) ?

The solution to 1/2 log_{10}(x+1)-2log_{10}(y-1) is log_{10}(((x+1)^{1/2})/((y-1)^2))

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simplify 1/2 log_{10}(x+1)-2log_{10}(y-1)

simplify

\frac{1}{2} lo g_{10} (x + 1) - 2 lo g_{10} (y - 1)

lo g_{10} (\frac{( x + 1 ) ^{\frac{1}{2}}}{( y - 1 ) ^{2}})

Solution steps

\frac{1}{2} lo g_{10} (x + 1) - 2 lo g_{10} (y - 1)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{\frac{1}{2}})

= lo g_{10} ((x + 1)^{\frac{1}{2}}) - 2 lo g_{10} (y - 1)

Apply log rule:

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

2 lo g_{10} (y - 1) = lo g_{10} ((y - 1)^{2})

= lo g_{10} ((x + 1)^{\frac{1}{2}}) - lo g_{10} ((y - 1)^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} ((x + 1)^{\frac{1}{2}}) - lo g_{10} ((y - 1)^{2}) = lo g_{10} (\frac{( x + 1 ) ^{\frac{1}{2}}}{( y - 1 ) ^{2}})

= lo g_{10} (\frac{( x + 1 ) ^{\frac{1}{2}}}{( y - 1 ) ^{2}})

lo g_{3} (\frac{1}{ln ( 3 )})

ln (\frac{1}{2 π ( x ^{2} ) ^{\frac{n}{2}}})

lo g_{b} (\frac{57}{74})

- ln (6) + ln (3)

ln (\frac{2950000 + 2200000}{2950000}) \cdot 2550

What is 1/2 log_{10}(x+1)-2log_{10}(y-1) ?
The solution to 1/2 log_{10}(x+1)-2log_{10}(y-1) is log_{10}(((x+1)^{1/2})/((y-1)^2))