What is expand log_{2}(((x-5)^3)^{1/2}) ?

The solution to expand log_{2}(((x-5)^3)^{1/2}) is 3/2 log_{2}(x-5)

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expand log_{2}(((x-5)^3)^{1/2})

expand

lo g_{2} (((x - 5)^{3})^{\frac{1}{2}})

\frac{3}{2} lo g_{2} (x - 5)

Solution steps

lo g_{2} (((x - 5)^{3})^{\frac{1}{2}})

Apply log rule:

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

lo g_{2} (((x - 5)^{3})^{\frac{1}{2}}) = \frac{1}{2} lo g_{2} ((x - 5)^{3})

= \frac{1}{2} lo g_{2} ((x - 5)^{3})

Apply log rule:

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

lo g_{2} ((x - 5)^{3}) = 3 lo g_{2} (x - 5)

= \frac{1}{2} \cdot 3 lo g_{2} (x - 5)

Multiply fractions:

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

= \frac{1 \cdot 3}{2} lo g_{2} (x - 5)

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{2} lo g_{2} (x - 5)

- 0.43 lo g_{2} (0.43) - 0.57 lo g_{2} (0.57)

lo g_{b} (x^{4} y)

4 lo g_{b} (y) + 6 lo g_{b} (w)

ln (\frac{e ^{4}}{3})

\frac{1}{5} (4 ln (x + 4) + ln (x - 1)) + c

What is expand log_{2}(((x-5)^3)^{1/2}) ?
The solution to expand log_{2}(((x-5)^3)^{1/2}) is 3/2 log_{2}(x-5)