What is 1/5 ln(x+1)+4/5 ln(x-4) ?

The solution to 1/5 ln(x+1)+4/5 ln(x-4) is ln((x+1)^{1/5}(x-4)^{4/5})

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simplify 1/5 ln(x+1)+4/5 ln(x-4)

simplify

\frac{1}{5} ln (x + 1) + \frac{4}{5} ln (x - 4)

ln ((x + 1)^{\frac{1}{5}} (x - 4)^{\frac{4}{5}})

Solution steps

\frac{1}{5} ln (x + 1) + \frac{4}{5} ln (x - 4)

Apply log rule:

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

\frac{1}{5} ln (x + 1) = ln ((x + 1)^{\frac{1}{5}})

= ln ((x + 1)^{\frac{1}{5}}) + \frac{4}{5} ln (x - 4)

Apply log rule:

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

\frac{4}{5} ln (x - 4) = ln ((x - 4)^{\frac{4}{5}})

= ln ((x + 1)^{\frac{1}{5}}) + ln ((x - 4)^{\frac{4}{5}})

Apply log rule:

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

ln ((x + 1)^{\frac{1}{5}}) + ln ((x - 4)^{\frac{4}{5}}) = ln ((x + 1)^{\frac{1}{5}} (x - 4)^{\frac{4}{5}})

= ln ((x + 1)^{\frac{1}{5}} (x - 4)^{\frac{4}{5}})

5 lo g_{7} (y) - \frac{3}{5} lo g_{7} (z)

lo g_{10} (\frac{[ 1.02 ]}{[ 0.875 ]}) + 4.757

3 ln (x) - ln (y)

- lo g_{10} (5 \cdot 1 0^{5})

\frac{1}{2} \cdot ln (\frac{x + 1}{x - 1})

What is 1/5 ln(x+1)+4/5 ln(x-4) ?
The solution to 1/5 ln(x+1)+4/5 ln(x-4) is ln((x+1)^{1/5}(x-4)^{4/5})