What is log_{x}(4a)+2log_{x}(a)-3log_{x}(a) ?

The solution to log_{x}(4a)+2log_{x}(a)-3log_{x}(a) is 2log_{x}(2)

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simplify log_{x}(4a)+2log_{x}(a)-3log_{x}(a)

simplify

lo g_{x} (4 a) + 2 lo g_{x} (a) - 3 lo g_{x} (a)

2 lo g_{x} (2)

Solution steps

lo g_{x} (4 a) + 2 lo g_{x} (a) - 3 lo g_{x} (a)

Add similar elements:

2 lo g_{x} (a) - 3 lo g_{x} (a) = - lo g_{x} (a)

= lo g_{x} (4 a) - lo g_{x} (a)

Apply log rule:

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

lo g_{x} (4 a) - lo g_{x} (a) = lo g_{x} (\frac{4 a}{a})

= lo g_{x} (\frac{4 a}{a})

Simplify

\frac{4 a}{a} : 4

= lo g_{x} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{x} (2)

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What is log_{x}(4a)+2log_{x}(a)-3log_{x}(a) ?
The solution to log_{x}(4a)+2log_{x}(a)-3log_{x}(a) is 2log_{x}(2)