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Popular >

simplify log_{4}(8x)

Solution

simplify

lo g_{4} (8 x)

Solution

1 + \frac{lo g _{2} ( x ) + 1}{2}

Solution steps

lo g_{4} (8 x)

Factor the number:

8 = 4 \cdot 2

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{4} (4) = 1

= 1 + lo g_{4} (2 x)

Simplify

lo g_{4} (2 x) : \frac{lo g _{2} ( x ) + 1}{2}

= 1 + \frac{lo g _{2} ( x ) + 1}{2}

Popular Examples

simplify log_{3}(9/y)simplify

lo g_{3} (\frac{9}{y})

simplify 1/2 log_{10}(a)+4log_{10}(b)simplify

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\frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (x + 1)

Frequently Asked Questions (FAQ)

What is log_{4}(8x) ?
The solution to log_{4}(8x) is 1+(log_{2}(x)+1)/2