What is simplify-1/2 ln(5-2x)-ln(x) ?

The solution to simplify-1/2 ln(5-2x)-ln(x) is -ln((5-2x)^{1/2}x)

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simplify-1/2 ln(5-2x)-ln(x)

simplify

- \frac{1}{2} ln (5 - 2 x) - ln (x)

- ln ((5 - 2 x)^{\frac{1}{2}} x)

Solution steps

- \frac{1}{2} ln (5 - 2 x) - ln (x)

Apply log rule:

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

\frac{1}{2} ln (- 2 x + 5) = ln ((- 2 x + 5)^{\frac{1}{2}})

= - ln ((- 2 x + 5)^{\frac{1}{2}}) - ln (x)

Rewrite

- ln ((- 2 x + 5)^{\frac{1}{2}}) - ln (x)

- (ln ((- 2 x + 5)^{\frac{1}{2}}) + ln (x))

= - (ln ((- 2 x + 5)^{\frac{1}{2}}) + ln (x))

Apply log rule:

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

ln ((5 - 2 x)^{\frac{1}{2}}) + ln (x) = ln (x (- 2 x + 5)^{\frac{1}{2}})

= - ln ((5 - 2 x)^{\frac{1}{2}} x)

ln ∣ x ∣ + 2 ln (x^{2} + 4) + C

ln (\frac{10}{22.5})

\frac{1}{5} ln (\frac{170 - 75}{115})

- lo g_{10} (8.45 \cdot 1 0^{- 6})

\frac{9}{14} \cdot lo g_{2} (\frac{9}{14}) + \frac{5}{14} \cdot lo g_{2} (\frac{5}{14})

What is simplify-1/2 ln(5-2x)-ln(x) ?
The solution to simplify-1/2 ln(5-2x)-ln(x) is -ln((5-2x)^{1/2}x)