What is expand log_{10}(sqrt(1000000x)) ?

The solution to expand log_{10}(sqrt(1000000x)) is 1/2 log_{10}(x)+3

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expand log_{10}(sqrt(1000000x))

expand

lo g_{10} (1000000 x)

\frac{1}{2} lo g_{10} (x) + 3

Solution steps

lo g_{10} (1000000 x)

1000000 x = 1000 x

= lo g_{10} (1000 x)

Apply log rule:

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

lo g_{10} (1000 x) = lo g_{10} (x) + lo g_{10} (1000)

= lo g_{10} (x) + lo g_{10} (1000)

Simplify

lo g_{10} (1000) : 3

Rewrite as

= lo g_{10} (x^{\frac{1}{2}}) + 3

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} lo g_{10} (x) + 3

p ro d u c t (1 + i) (2 - 3 i)

\frac{( 7 x ^{2} )}{( x - 4 ) ^{2} ( x + 4 ) ^{2}}

\frac{s + 10}{( x + 2 ) ( s + 3 )}

\frac{9 e ^{- 2 s}}{( s - 2 ) ( s + 7 )}

d x (x^{2} + 1)

What is expand log_{10}(sqrt(1000000x)) ?
The solution to expand log_{10}(sqrt(1000000x)) is 1/2 log_{10}(x)+3