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)

Rewrite

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

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

= - 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)))

Apply rule

- (- a) = a

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

2 ln (3) + ln (5)

lo g_{10} (\frac{x ^{2} y ^{5}}{z})

7 \cdot ln (a) - 4 \cdot ln (b)

lo g_{b} (x + 1) - lo g_{b} (x)

lo g_{6} (x) - lo g_{6} (x^{2})

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))}