What is expand log_{10}(sqrt(10000z)) ?

The solution to expand log_{10}(sqrt(10000z)) is 1/2 log_{10}(z)+2

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expand log_{10}(sqrt(10000z))

expand

lo g_{10} (10000 z)

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

Solution steps

lo g_{10} (10000 z)

10000 z = 100 z

= lo g_{10} (100 z)

Apply log rule:

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

lo g_{10} (100 z) = lo g_{10} (z) + lo g_{10} (100)

= lo g_{10} (z) + lo g_{10} (100)

Simplify

lo g_{10} (100) : 2

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

ln (2 x + 4) (3 x - 1)

\frac{( 3 x - 5 ) ( 4 x + 1 )}{( 2 x + 3 ) ( 5 x - 2 )}

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(x^{2} + 1 + x^{2} - 1)^{2}

\frac{27 x ^{4}}{( 15 - x ) ^{2}}

What is expand log_{10}(sqrt(10000z)) ?
The solution to expand log_{10}(sqrt(10000z)) is 1/2 log_{10}(z)+2