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

The solution to ln(x)-1/2 ln(2x+1)-1/2 ln(2x+3) is ln((xsqrt(2x+1)sqrt(2x+3))/((2x+1)(2x+3)))

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Simplify

\frac{x}{( 2 x + 1 ) ^{\frac{1}{2}}} : \frac{x 2 x + 1}{2 x + 1}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Simplify

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

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

ln (\frac{( 1 \cdot 1 0 ^{- 7} )}{0.001})

ln (\frac{5 y - 8}{y})

2 ln (a^{3} b^{4}) - 3 ln (a) - 3 ln (a b^{2})

ln (\frac{5}{14})

\frac{( - \frac{1}{2} ln ( x ) - \frac{1}{4} ln ( 2 + x ^{2} ) )}{e}

What is ln(x)-1/2 ln(2x+1)-1/2 ln(2x+3) ?
The solution to ln(x)-1/2 ln(2x+1)-1/2 ln(2x+3) is ln((xsqrt(2x+1)sqrt(2x+3))/((2x+1)(2x+3)))