What is log_{2}(x+1)+3log_{2}(x)-8log_{4}(x) ?

The solution to log_{2}(x+1)+3log_{2}(x)-8log_{4}(x) is log_{2}((x+1)x^3)-8log_{4}(x)

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simplify log_{2}(x+1)+3log_{2}(x)-8log_{4}(x)

simplify

lo g_{2} (x + 1) + 3 lo g_{2} (x) - 8 lo g_{4} (x)

lo g_{2} ((x + 1) x^{3}) - 8 lo g_{4} (x)

Solution steps

lo g_{2} (x + 1) + 3 lo g_{2} (x) - 8 lo g_{4} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{2} (x) = lo g_{2} (x^{3})

= lo g_{2} (x + 1) + lo g_{2} (x^{3}) - 8 lo g_{4} (x)

Apply log rule:

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

lo g_{2} (x + 1) + lo g_{2} (x^{3}) = lo g_{2} (x^{3} (x + 1))

= lo g_{2} ((x + 1) x^{3}) - 8 lo g_{4} (x)

\frac{1}{2} lo g_{10} (c) + 5 lo g_{10} (d)

lo g_{6} (x^{4} y^{6})

4 ln (x) - \frac{1}{8} ln (y)

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{10} (\frac{x ^{2}}{2})

What is log_{2}(x+1)+3log_{2}(x)-8log_{4}(x) ?
The solution to log_{2}(x+1)+3log_{2}(x)-8log_{4}(x) is log_{2}((x+1)x^3)-8log_{4}(x)