What is expand log_{10}(sqrt(a^9b)) ?

The solution to expand log_{10}(sqrt(a^9b)) is 4log_{10}(a)+1/2 log_{10}(ab)

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expand log_{10}(sqrt(a^9b))

expand

lo g_{10} (a^{9} b)

4 lo g_{10} (a) + \frac{1}{2} lo g_{10} (ab)

Solution steps

lo g_{10} (a^{9} b)

a^{9} b = a^{4} ab

= lo g_{10} (a^{4} ab)

Apply log rule:

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

lo g_{10} (a^{4} ab) = lo g_{10} (ab) + lo g_{10} (a^{4})

= lo g_{10} (ab) + lo g_{10} (a^{4})

Apply log rule:

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

lo g_{10} (ab) + lo g_{10} (a^{4}) = lo g_{10} (a^{4} ab)

= lo g_{10} (ab a^{4})

Apply log rule:

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

lo g_{10} (ab a^{4}) = lo g_{10} (a^{4}) + lo g_{10} (ab)

= lo g_{10} (a^{4}) + lo g_{10} (ab)

Simplify

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

= lo g_{10} (a^{4}) + \frac{1}{2} lo g_{10} (ab)

Apply log rule

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

assuming

x \geq 0

= 4 lo g_{10} (a) + \frac{1}{2} lo g_{10} (ab)

s im p l^{12} (\frac{8 x}{4} - 3)

\frac{2}{( 1 + x ^{2} + y ^{2} ) ^{2}}

2 (2 ln (2) + 1)

6 (14 ln (2) - 3)

\frac{4 ( 2 s + 10 ) ( 2 s - 80 )}{s ^{2} - 3200}

What is expand log_{10}(sqrt(a^9b)) ?
The solution to expand log_{10}(sqrt(a^9b)) is 4log_{10}(a)+1/2 log_{10}(ab)