What is 1/2 ln(x)+3ln(5) ?

The solution to 1/2 ln(x)+3ln(5) is ln(125x^{1/2})

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simplify 1/2 ln(x)+3ln(5)

simplify

\frac{1}{2} ln (x) + 3 ln (5)

ln (125 x^{\frac{1}{2}})

Solution steps

\frac{1}{2} ln (x) + 3 ln (5)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}}) + 3 ln (5)

Apply log rule:

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

3 ln (5) = ln (5^{3})

= ln (x^{\frac{1}{2}}) + ln (5^{3})

Apply log rule:

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

ln (x^{\frac{1}{2}}) + ln (5^{3}) = ln (5^{3} x^{\frac{1}{2}})

= ln (5^{3} x^{\frac{1}{2}})

5^{3} = 125

= ln (125 x^{\frac{1}{2}})

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