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

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

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expand log_{10}(z^7x)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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} (x)

ln (\frac{x ^{3} - 2}{x ^{4}})

ln (2) + ln (2 x)

ln (765 e^{- \frac{120}{x}})

- \frac{3}{2} ln w^{2} + 1 + 3 ln (w)

13 lo g_{10} (a) - 2 lo g_{10} (b) + lo g_{10} (c)

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