What is ln(x^5*250^{5x}*1/(403^{x+1)}) ?

The solution to ln(x^5*250^{5x}*1/(403^{x+1)}) is 5ln(x)+5xln(250)++ln(1)-(x+1)ln(403)

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simplify ln(x^5250^{5x}1/(403^{x+1)})

simplify

ln (x^{5} \cdot 25 0^{5 x} \cdot \frac{1}{40 3 ^{x + 1}})

5 ln (x) + 5 x ln (250) + + ln (1) - (x + 1) ln (403)

Solution steps

ln (x^{5} \cdot 25 0^{5 x} \cdot \frac{1}{40 3 ^{x + 1}})

Apply log rule:

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

ln (x^{5} \cdot 25 0^{5 x} \cdot \frac{1}{40 3 ^{x + 1}}) = ln (x^{5}) + ln (25 0^{5 x}) + ln (\frac{1}{40 3 ^{x + 1}})

= ln (x^{5}) + ln (25 0^{5 x}) + ln (\frac{1}{40 3 ^{x + 1}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= 5 ln (x) + ln (25 0^{5 x}) + ln (\frac{1}{40 3 ^{x + 1}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (25 0^{5 x}) = 5 x ln (250)

= 5 ln (x) + 5 x ln (250) + ln (\frac{1}{40 3 ^{x + 1}})

Apply log rule:

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

ln (\frac{1}{40 3 ^{x + 1}}) = ln (1) - ln (40 3^{x + 1})

= 5 ln (x) + 5 ln (250) x + + ln (1) - ln (40 3^{x + 1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (40 3^{x + 1}) = (x + 1) ln (403)

= 5 ln (x) + 5 x ln (250) + + ln (1) - (x + 1) ln (403)

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\frac{7.2}{150} ln (\frac{1}{0.03})

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2 ln (x^{3} + 2) + 2 - 2 ln (- x^{2} + 2 x + 2) - 2

lo g_{5} (x + 3) + lo g_{5} (x - 3)

What is ln(x^5*250^{5x}*1/(403^{x+1)}) ?
The solution to ln(x^5*250^{5x}*1/(403^{x+1)}) is 5ln(x)+5xln(250)++ln(1)-(x+1)ln(403)