What is log_{1/6}(4)+log_{1/6}(9) ?

The solution to log_{1/6}(4)+log_{1/6}(9) is -2

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simplify log_{1/6}(4)+log_{1/6}(9)

simplify

lo g_{\frac{1}{6}} (4) + lo g_{\frac{1}{6}} (9)

- 2

Solution steps

lo g_{\frac{1}{6}} (4) + lo g_{\frac{1}{6}} (9)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{\frac{1}{6}} (4) + lo g_{\frac{1}{6}} (9) = lo g_{\frac{1}{6}} (4 \cdot 9)

= lo g_{\frac{1}{6}} (4 \cdot 9)

Apply log rule:

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

lo g_{\frac{1}{6}} (4 \cdot 9) = - lo g_{6} (4 \cdot 9)

= - lo g_{6} (4 \cdot 9)

Multiply the numbers:

4 \cdot 9 = 36

= - lo g_{6} (36)

Factor the number:

36 = 6^{2}

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

Apply log rule:

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

lo g_{6} (6^{2}) = 2

= - 2

\frac{5 y}{x} + \frac{3 x}{y}

35 \div 7

e^{2 l n (y)}

\frac{2 x + 1}{x - 5} + \frac{2}{x}

What is log_{1/6}(4)+log_{1/6}(9) ?
The solution to log_{1/6}(4)+log_{1/6}(9) is -2