What is expand log_{10}(z^4sqrt(y*x^9)) ?

The solution to expand log_{10}(z^4sqrt(y*x^9)) is 4log_{10}(z)+log_{10}(sqrt(y)sqrt(x)sqrt(x^8))

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expand log_{10}(z^4sqrt(y*x^9))

expand

lo g_{10} (z^{4} y \cdot x^{9})

4 lo g_{10} (z) + lo g_{10} (y x x^{8})

Solution steps

lo g_{10} (z^{4} y x^{9})

Apply log rule:

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

lo g_{10} (z^{4} y x^{9}) = lo g_{10} (z^{4}) + lo g_{10} (y x^{9})

= lo g_{10} (z^{4}) + lo g_{10} (y x^{9})

Apply log rule:

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

lo g_{10} (z^{4}) = 4 lo g_{10} (z)

= 4 lo g_{10} (z) + lo g_{10} (y x^{9})

y x^{9} = y x x^{8}

= 4 lo g_{10} (z) + lo g_{10} (y x x^{8})

2550 \cdot ln (\frac{2950000}{2950000 - 2200000})

ln (\frac{500}{250})

lo g_{3} (A^{4} B^{9})

2 \cdot lo g_{10} (x) - lo g_{10} (x + 6)

lo g_{e} (\frac{( x ^{2} \cdot y ^{3} )}{z ^{4}})

What is expand log_{10}(z^4sqrt(y*x^9)) ?
The solution to expand log_{10}(z^4sqrt(y*x^9)) is 4log_{10}(z)+log_{10}(sqrt(y)sqrt(x)sqrt(x^8))