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Popular >

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

Solution

simplify

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

Solution

ln (8 x^{\frac{1}{2}})

Solution steps

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

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 (2)

Apply log rule:

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

3 ln (2) = ln (2^{3})

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

Apply log rule:

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

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

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

2^{3} = 8

= ln (8 x^{\frac{1}{2}})

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Frequently Asked Questions (FAQ)

What is 1/2 ln(x)+3ln(2) ?
The solution to 1/2 ln(x)+3ln(2) is ln(8x^{1/2})