What is expand log_{10}(sqrt(x^5yz^3)) ?

The solution to expand log_{10}(sqrt(x^5yz^3)) is log_{10}(z)+2log_{10}(x)+1/2 log_{10}(xyz)

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expand log_{10}(sqrt(x^5yz^3))

expand

lo g_{10} (x^{5} y z^{3})

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

Solution steps

lo g_{10} (x^{5} y z^{3})

x^{5} y z^{3} = x^{2} z x yz

= lo g_{10} (x^{2} z x yz)

Apply log rule:

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

lo g_{10} (x^{2} x yz z) = lo g_{10} (x yz z) + lo g_{10} (x^{2})

= lo g_{10} (z x yz) + lo g_{10} (x^{2})

Apply log rule:

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

lo g_{10} (z x yz) + lo g_{10} (x^{2}) = lo g_{10} (x^{2} z x yz)

= lo g_{10} (x yz z x^{2})

Apply log rule:

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

lo g_{10} (x yz z x^{2}) = lo g_{10} (z x^{2}) + lo g_{10} (x yz)

= lo g_{10} (x^{2} z) + lo g_{10} (x yz)

Simplify

lo g_{10} (x yz) : \frac{1}{2} lo g_{10} (x yz)

= lo g_{10} (x^{2} z) + \frac{1}{2} lo g_{10} (x yz)

lo g_{10} (z x^{2}) = lo g_{10} (z) + 2 lo g_{10} (x)

= lo g_{10} (z) + 2 lo g_{10} (x) + \frac{1}{2} lo g_{10} (x yz)

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\frac{2 ( x ^{2} - 9 )}{x ^{2} - 4}

\frac{x ^{2} + 5}{( x - 1 ) ( x ^{2} + 4 ) ^{2}}

\frac{( 2 - x ) ^{2}}{2}

What is expand log_{10}(sqrt(x^5yz^3)) ?
The solution to expand log_{10}(sqrt(x^5yz^3)) is log_{10}(z)+2log_{10}(x)+1/2 log_{10}(xyz)