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

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

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

expand

lo g_{10} (10000 y)

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

Solution steps

lo g_{10} (10000 y)

10000 y = 100 y

= lo g_{10} (100 y)

Apply log rule:

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

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

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

Simplify

lo g_{10} (100) : 2

Rewrite as

= lo g_{10} (y^{\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} (y) + 2

f (1 - 2)

f (0, - e^{π}) - f (0, 1)

\frac{( n ^{2} - 9 ) ^{2}}{9 n ^{2}}

\frac{2 ( 45 - 2 15 )}{15}

π (e^{2} - 1)

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