What is 2ln(x+49)-4ln(x-7) ?

The solution to 2ln(x+49)-4ln(x-7) is ln(((x+49)^2)/((x-7)^4))

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simplify 2ln(x+49)-4ln(x-7)

simplify

2 ln (x + 49) - 4 ln (x - 7)

ln (\frac{( x + 49 ) ^{2}}{( x - 7 ) ^{4}})

Solution steps

2 ln (x + 49) - 4 ln (x - 7)

Apply log rule:

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

2 ln (x + 49) = ln ((x + 49)^{2})

= ln ((x + 49)^{2}) - 4 ln (x - 7)

Apply log rule:

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

4 ln (x - 7) = ln ((x - 7)^{4})

= ln ((x + 49)^{2}) - ln ((x - 7)^{4})

Apply log rule:

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

ln ((x + 49)^{2}) - ln ((x - 7)^{4}) = ln (\frac{( x + 49 ) ^{2}}{( x - 7 ) ^{4}})

= ln (\frac{( x + 49 ) ^{2}}{( x - 7 ) ^{4}})

ln (x - 5) + ln (x + 5)

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

lo g_{b} (x^{2} y)

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

lo g_{a} (\frac{x ^{5}}{y z ^{6}})

What is 2ln(x+49)-4ln(x-7) ?
The solution to 2ln(x+49)-4ln(x-7) is ln(((x+49)^2)/((x-7)^4))