What is expand log_{10}(z^7y) ?

The solution to expand log_{10}(z^7y) is 7log_{10}(z)+log_{10}(y)

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expand log_{10}(z^7y)

expand

lo g_{10} (z^{7} y)

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

Solution steps

lo g_{10} (z^{7} y)

Apply log rule:

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

lo g_{10} (z^{7} y) = lo g_{10} (z^{7}) + lo g_{10} (y)

= lo g_{10} (z^{7}) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (z^{7}) = 7 lo g_{10} (z)

= 7 lo g_{10} (z) + lo g_{10} (y)

ln (\frac{x - 1}{x - 2})

- \frac{8}{14} lo g_{2} (\frac{8}{14}) - \frac{6}{14} lo g_{2} (\frac{6}{14})

lo g_{10} (\frac{5}{36}) - lo g_{10} (\frac{5}{9})

- \frac{1}{44.6} ln (\frac{1}{2})

lo g_{5} (\frac{x}{x + 2})

What is expand log_{10}(z^7y) ?
The solution to expand log_{10}(z^7y) is 7log_{10}(z)+log_{10}(y)