What is 1/2 ln(9x^2)+ln(3x) ?

The solution to 1/2 ln(9x^2)+ln(3x) is ln(9x^2)

Popular >

simplify 1/2 ln(9x^2)+ln(3x)

simplify

\frac{1}{2} ln (9 x^{2}) + ln (3 x)

ln (9 x^{2})

Solution steps

\frac{1}{2} ln (9 x^{2}) + ln (3 x)

Apply log rule:

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

\frac{1}{2} ln (9 x^{2}) = ln ((9 x^{2})^{\frac{1}{2}})

= ln ((9 x^{2})^{\frac{1}{2}}) + ln (3 x)

Apply log rule:

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

ln ((9 x^{2})^{\frac{1}{2}}) + ln (3 x) = ln (3 x (9 x^{2})^{\frac{1}{2}})

= ln (3 x (9 x^{2})^{\frac{1}{2}})

Simplify

(9 x^{2})^{\frac{1}{2}} \cdot 3 x : 9 x^{2}

= ln (9 x^{2})

ln (\frac{( 2 x + 3 ) ( x + 6 ) ^{4}}{( 1 - 4 x ) ^{5}})

ln (x^{2} - 1) - ln (x + 1) + ln (x^{2} + 1)

5 lo g_{4} (x) - lo g_{4} (6)

ln (\frac{2 \cdot 1 0 ^{6}}{1 0 ^{6}})

- lo g_{10} (3.9 \cdot 1 0^{- 8})