What is expand log_{b}((sqrt(x))/((yz)^2)) ?

The solution to expand log_{b}((sqrt(x))/((yz)^2)) is log_{b}(sqrt(x))-2log_{b}(y)-2log_{b}(z)

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expand log_{b}((sqrt(x))/((yz)^2))

expand

lo g_{b} (\frac{x}{( yz ) ^{2}})

lo g_{b} (x) - 2 lo g_{b} (y) - 2 lo g_{b} (z)

Solution steps

lo g_{b} (\frac{x}{( yz ) ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{b} (\frac{x}{( yz ) ^{2}}) = lo g_{b} (x) - lo g_{b} ((yz)^{2})

= lo g_{b} (x) - lo g_{b} ((yz)^{2})

Apply log rule:

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

lo g_{b} ((yz)^{2}) = 2 lo g_{b} (yz)

= lo g_{b} (x) - 2 lo g_{b} (yz)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

2 lo g_{b} (yz) = 2 lo g_{b} (y) + 2 lo g_{b} (z)

= lo g_{b} (x) - (2 lo g_{b} (y) + 2 lo g_{b} (z))

- (2 lo g_{b} (y) + 2 lo g_{b} (z)) : - 2 lo g_{b} (y) - 2 lo g_{b} (z)

= lo g_{b} (x) - 2 lo g_{b} (y) - 2 lo g_{b} (z)

2 lo g_{10} (x) - 7 lo g_{10} (y)

ln (x^{5}) - ln (x)

\frac{1}{2} lo g_{b} (57) + \frac{1}{2} lo g_{b} (74)

ln (2 e^{2 x})

lo g_{10} ((u v^{6})^{4})

What is expand log_{b}((sqrt(x))/((yz)^2)) ?
The solution to expand log_{b}((sqrt(x))/((yz)^2)) is log_{b}(sqrt(x))-2log_{b}(y)-2log_{b}(z)