What is 3/2 log_{10}(x+4)-3log_{10}(x)-ln(6) ?

The solution to 3/2 log_{10}(x+4)-3log_{10}(x)-ln(6) is log_{10}(((x+4)^{3/2})/(x^3))-ln(6)

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simplify 3/2 log_{10}(x+4)-3log_{10}(x)-ln(6)

simplify

\frac{3}{2} lo g_{10} (x + 4) - 3 lo g_{10} (x) - ln (6)

lo g_{10} (\frac{( x + 4 ) ^{\frac{3}{2}}}{x ^{3}}) - ln (6)

Solution steps

\frac{3}{2} lo g_{10} (x + 4) - 3 lo g_{10} (x) - ln (6)

Apply log rule:

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

\frac{3}{2} lo g_{10} (x + 4) = lo g_{10} ((x + 4)^{\frac{3}{2}})

= lo g_{10} ((x + 4)^{\frac{3}{2}}) - 3 lo g_{10} (x) - ln (6)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} ((x + 4)^{\frac{3}{2}}) - lo g_{10} (x^{3}) - ln (6)

Apply log rule:

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

lo g_{10} ((x + 4)^{\frac{3}{2}}) - lo g_{10} (x^{3}) = lo g_{10} (\frac{( x + 4 ) ^{\frac{3}{2}}}{x ^{3}})

= lo g_{10} (\frac{( x + 4 ) ^{\frac{3}{2}}}{x ^{3}}) - ln (6)

1 + 12 lo g_{2} (\frac{261.1}{27.5})

- 1.5 - lo g_{10} (1.3 \cdot 1 0^{10})

lo g_{10} (\frac{1}{900})

\frac{d}{d y} ((x) (ln (x) - ln (y)))

What is 3/2 log_{10}(x+4)-3log_{10}(x)-ln(6) ?
The solution to 3/2 log_{10}(x+4)-3log_{10}(x)-ln(6) is log_{10}(((x+4)^{3/2})/(x^3))-ln(6)