What is sqrt(1+log_{1/3)(x)+log_{1/3}(x+2)} ?

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

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simplify sqrt(1+log_{1/3)(x)+log_{1/3}(x+2)}

simplify

1 + lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2)

1 - lo g_{3} (x (x + 2))

Solution steps

1 + lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2)

Apply log rule:

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

lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2) = lo g_{\frac{1}{3}} (x (x + 2))

= 1 + lo g_{\frac{1}{3}} (x (x + 2))

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

= 1 - lo g_{3} (x (x + 2))

2 lo g_{b} (6) - lo g_{b} (9)

\frac{1}{2} lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

ln (\frac{81}{125})

ln (x) - 2 ln (y)

lo g_{10} (\frac{a ^{6}}{b ^{5} c})

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