What is log_{10}((x^4y)/z) ?

The solution to log_{10}((x^4y)/z) is 4log_{10}(x)+log_{10}(y)-log_{10}(z)

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simplify log_{10}((x^4y)/z)

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x ^{4} y}{z}) = lo g_{10} (x^{4} y) - lo g_{10} (z)

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

Simplify

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

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

\frac{1}{2} lo g_{a} (x) - 3 lo g_{a} (y) + 6 lo g_{a} (z)

- lo g_{b} (\frac{1}{8})

ln (x) + ln (x - 1)

1 + lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 2)

2 lo g_{b} (6) - lo g_{b} (9)

What is log_{10}((x^4y)/z) ?
The solution to log_{10}((x^4y)/z) is 4log_{10}(x)+log_{10}(y)-log_{10}(z)