What is expand log_{10}(z^9y) ?

The solution to expand log_{10}(z^9y) is 9log_{10}(z)+log_{10}(y)

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expand log_{10}(z^9y)

expand

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

9 lo g_{10} (z) + lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (z^{9}) = 9 lo g_{10} (z)

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

lo g_{3} (4 ab)

3.79 + lo g_{10} (\frac{0.2 + 0.02}{0.5 - 0.02})

2 lo g_{5} (2) + 3 lo g_{5} (3)

lo g_{3} (9) + lo g_{4} (\frac{1}{6}) + lo g_{5} (1)

- \frac{1}{3} ln (\frac{1}{3})

What is expand log_{10}(z^9y) ?
The solution to expand log_{10}(z^9y) is 9log_{10}(z)+log_{10}(y)