What is 4ln(x+3)-1/5 ln(4x+7) ?

The solution to 4ln(x+3)-1/5 ln(4x+7) is ln(((x+3)^4(4x+7)^{4/5})/(4x+7))

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simplify 4ln(x+3)-1/5 ln(4x+7)

simplify

4 ln (x + 3) - \frac{1}{5} ln (4 x + 7)

ln (\frac{( x + 3 ) ^{4} ( 4 x + 7 ) ^{\frac{4}{5}}}{4 x + 7})

Solution steps

4 ln (x + 3) - \frac{1}{5} ln (4 x + 7)

Apply log rule:

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

4 ln (x + 3) = ln ((x + 3)^{4})

= ln ((x + 3)^{4}) - \frac{1}{5} ln (4 x + 7)

Apply log rule:

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

\frac{1}{5} ln (4 x + 7) = ln ((4 x + 7)^{\frac{1}{5}})

= ln ((x + 3)^{4}) - ln ((4 x + 7)^{\frac{1}{5}})

Apply log rule:

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

ln ((x + 3)^{4}) - ln ((4 x + 7)^{\frac{1}{5}}) = ln (\frac{( x + 3 ) ^{4}}{( 4 x + 7 ) ^{\frac{1}{5}}})

= ln (\frac{( x + 3 ) ^{4}}{( 4 x + 7 ) ^{\frac{1}{5}}})

Simplify

\frac{( x + 3 ) ^{4}}{( 4 x + 7 ) ^{\frac{1}{5}}} : \frac{( x + 3 ) ^{4} ( 4 x + 7 ) ^{\frac{4}{5}}}{4 x + 7}

= ln (\frac{( x + 3 ) ^{4} ( 4 x + 7 ) ^{\frac{4}{5}}}{4 x + 7})

2 lo g_{2} (3) - lo g_{2} (5)

lo g_{10} (2) + lo g_{10} (11)

lo g_{7} (9) - lo g_{7} (8)

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

- \frac{ln ( 531441 g )}{3 ln ( 3 ) - ln ( g )}

What is 4ln(x+3)-1/5 ln(4x+7) ?
The solution to 4ln(x+3)-1/5 ln(4x+7) is ln(((x+3)^4(4x+7)^{4/5})/(4x+7))