What is log_{10}(y/(x^7)) ?

The solution to log_{10}(y/(x^7)) is log_{10}(y)-7log_{10}(x)

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simplify log_{10}(y/(x^7))

simplify

lo g_{10} (\frac{y}{x ^{7}})

lo g_{10} (y) - 7 lo g_{10} (x)

Solution steps

lo g_{10} (\frac{y}{x ^{7}})

Apply log rule:

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

lo g_{10} (\frac{y}{x ^{7}}) = lo g_{10} (y) - lo g_{10} (x^{7})

= lo g_{10} (y) - lo g_{10} (x^{7})

Simplify

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

= lo g_{10} (y) - 7 lo g_{10} (x)

lo g_{10} (3) + 2 lo g_{10} (x) + 3 lo g_{10} (y)

6 [ln (z) + ln (z + 7)] - 3 ln (z - 7)

ln (x \frac{y}{2})

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

ln (e^{iπ}) - ln (3 e^{iπ} + 4)

What is log_{10}(y/(x^7)) ?
The solution to log_{10}(y/(x^7)) is log_{10}(y)-7log_{10}(x)