What is log_{10}((4x^6)/(-1)) ?

The solution to log_{10}((4x^6)/(-1)) is 2log_{10}(2)+6log_{10}(x)-log_{10}(-1)

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simplify log_{10}((4x^6)/(-1))

simplify

lo g_{10} (\frac{4 x ^{6}}{- 1})

2 lo g_{10} (2) + 6 lo g_{10} (x) - lo g_{10} (- 1)

Solution steps

lo g_{10} (\frac{4 x ^{6}}{- 1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{4 x ^{6}}{- 1}) = lo g_{10} (4 x^{6}) - lo g_{10} (- 1)

= lo g_{10} (4 x^{6}) - lo g_{10} (- 1)

Apply log rule:

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

lo g_{10} (4 x^{6}) = lo g_{10} (4) + lo g_{10} (x^{6})

= lo g_{10} (4) + lo g_{10} (x^{6}) - lo g_{10} (- 1)

Apply log rule:

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

lo g_{10} (x^{6}) = 6 lo g_{10} (x)

= lo g_{10} (4) + 6 lo g_{10} (x) - lo g_{10} (- 1)

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) + 6 lo g_{10} (x) - lo g_{10} (- 1)

2 lo g_{8} (z) - \frac{1}{2} lo g_{8} (w) + 4 lo g_{8} (x)

2^{\frac{π}{2}} lo g_{10} (2)

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

ln (\frac{10}{22}) \cdot 5

ln (a \cdot b \cdot c)

What is log_{10}((4x^6)/(-1)) ?
The solution to log_{10}((4x^6)/(-1)) is 2log_{10}(2)+6log_{10}(x)-log_{10}(-1)