What is simplify-1/4 ln(2t-1)+3/4 ln(2t+1) ?

The solution to simplify-1/4 ln(2t-1)+3/4 ln(2t+1) is ln(\sqrt[4]{((2t+1)^3)/(2t-1)})

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simplify-1/4 ln(2t-1)+3/4 ln(2t+1)

simplify

- \frac{1}{4} ln (2 t - 1) + \frac{3}{4} ln (2 t + 1)

Solution steps

- \frac{1}{4} ln (2 t - 1) + \frac{3}{4} ln (2 t + 1)

Apply log rule:

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

\frac{1}{4} ln (2 t - 1) = ln ((2 t - 1)^{\frac{1}{4}})

= - ln ((2 t - 1)^{\frac{1}{4}}) + \frac{3}{4} ln (2 t + 1)

Apply log rule:

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

\frac{3}{4} ln (2 t + 1) = ln ((2 t + 1)^{\frac{3}{4}})

= - ln ((2 t - 1)^{\frac{1}{4}}) + ln ((2 t + 1)^{\frac{3}{4}})

Apply log rule:

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

ln ((2 t + 1)^{\frac{3}{4}}) - ln ((2 t - 1)^{\frac{1}{4}}) = ln (\frac{( 2 t + 1 ) ^{\frac{3}{4}}}{( 2 t - 1 ) ^{\frac{1}{4}}})

= ln (\frac{( 2 t + 1 ) ^{\frac{3}{4}}}{( 2 t - 1 ) ^{\frac{1}{4}}})

Combine same powers :

2 lo g_{0.29} (2) - lo g_{0.29} (13)

lo g_{10} (x^{2} y z^{3})

(ln (1.3) - ln (0.54)) \cdot 182000

ln (\frac{y ^{3}}{7})

lo g_{w} (\frac{13 w}{2})

What is simplify-1/4 ln(2t-1)+3/4 ln(2t+1) ?
The solution to simplify-1/4 ln(2t-1)+3/4 ln(2t+1) is ln(\sqrt[4]{((2t+1)^3)/(2t-1)})