What is expand log_{10}(z^8y) ?

The solution to expand log_{10}(z^8y) is 8log_{10}(z)+log_{10}(y)

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expand log_{10}(z^8y)

expand

lo g_{10} (z^{8} y)

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

Solution steps

lo g_{10} (z^{8} y)

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (z^{8}) = 8 lo g_{10} (z)

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

3 ln (3) + ln (2^{7})

ln (10) + 2 ln (x) + 3 ln (x^{2} + 10)

2 ln (2) + ln (\frac{5}{3})

\frac{14 ln ( x + h ) - 14 ln ( x )}{h}

lo g_{10} (557) 3

What is expand log_{10}(z^8y) ?
The solution to expand log_{10}(z^8y) is 8log_{10}(z)+log_{10}(y)