What is expand log_{b}((x+3)^{1/2})(2x) ?

The solution to expand log_{b}((x+3)^{1/2})(2x) is xlog_{b}(x+3)

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expand log_{b}((x+3)^{1/2})(2x)

expand

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

x lo g_{b} (x + 3)

Solution steps

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

Apply log rule:

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

lo g_{b} ((x + 3)^{\frac{1}{2}}) = \frac{1}{2} lo g_{b} (x + 3)

= \frac{1}{2} lo g_{b} (x + 3) \cdot 2 x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2 x}{2} lo g_{b} (x + 3)

Cancel the common factor:

2

= lo g_{b} (x + 3) \cdot 1 \cdot x

Multiply:

1 \cdot x = x

= x lo g_{b} (x + 3)

8 lo g_{10} (a) + lo g_{10} (d)

ln (2 x^{3})

lo g_{3} (v) - 4 lo g_{3} (w)

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y) - 4 lo g_{10} (z)

4 lo g_{10} (2) - 2 lo g_{10} (3) - lo g_{10} (4)

What is expand log_{b}((x+3)^{1/2})(2x) ?
The solution to expand log_{b}((x+3)^{1/2})(2x) is xlog_{b}(x+3)