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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

lo g_{7} (x y)

2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (\frac{x ^{5}}{z y})

ln (x) - ln (12)

ln (x) - ln (17)

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