What is log_{4}(x)+log_{4}(5)+log_{4}(2) ?

The solution to log_{4}(x)+log_{4}(5)+log_{4}(2) is log_{4}(10x)

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simplify log_{4}(x)+log_{4}(5)+log_{4}(2)

simplify

lo g_{4} (x) + lo g_{4} (5) + lo g_{4} (2)

lo g_{4} (10 x)

Solution steps

lo g_{4} (x) + lo g_{4} (5) + lo g_{4} (2)

Apply log rule:

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

lo g_{4} (x) + lo g_{4} (5) = lo g_{4} (x \cdot 5)

= lo g_{4} (x \cdot 5) + lo g_{4} (2)

Apply log rule:

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

lo g_{4} (x \cdot 5) + lo g_{4} (2) = lo g_{4} (x \cdot 5 \cdot 2)

= lo g_{4} (x \cdot 5 \cdot 2)

Simplify

x \cdot 5 \cdot 2 : 10 x

= lo g_{4} (10 x)

ln (- 4 e^{2 x})

10 lo g_{10} (\frac{x}{100000})

lo g_{10} (296) - lo g_{10} (23)

2 lo g_{5} (x) + \frac{1}{2} lo g_{5} (y) - 4 lo g_{5} (x)

lo g_{4} (\frac{16}{x + 9})

What is log_{4}(x)+log_{4}(5)+log_{4}(2) ?
The solution to log_{4}(x)+log_{4}(5)+log_{4}(2) is log_{4}(10x)