What is e^{(5/4 (ln(x)-ln(5x-4))+c)} ?

The solution to e^{(5/4 (ln(x)-ln(5x-4))+c)} is e^c(x/(5x-4))^{5/4}

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simplify e^{(5/4 (ln(x)-ln(5x-4))+c)}

simplify

e^{(\frac{5}{4} (l n (x) - l n (5 x - 4)) + c)}

e^{c} (\frac{x}{5 x - 4})^{\frac{5}{4}}

Solution steps

e^{(\frac{5}{4} (l n (x) - l n (5 x - 4)) + c)}

Apply log rule:

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

ln (x) - ln (5 x - 4) = ln (\frac{x}{5 x - 4})

= e^{\frac{5}{4} l n (\frac{x}{5 x - 4}) + c}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{\frac{5}{4} l n (\frac{x}{5 x - 4})} e^{c}

Simplify

e^{\frac{5}{4} l n (\frac{x}{5 x - 4})} : (\frac{x}{5 x - 4})^{\frac{5}{4}}

= (\frac{x}{5 x - 4})^{\frac{5}{4}} e^{c}

= e^{c} (\frac{x}{5 x - 4})^{\frac{5}{4}}

ln (\frac{2 ^{4}}{3 ^{3} 5 ^{3}})

lo g_{10} (5. 1^{2}) + lo g_{10} (2. 6^{4})

3 ln (\frac{5}{2}) + 4 ln (\frac{14}{11})

ln (\frac{18}{22})

ln (5 e) - ln (1 0^{3}) + lo g_{2} (4^{2})

What is e^{(5/4 (ln(x)-ln(5x-4))+c)} ?
The solution to e^{(5/4 (ln(x)-ln(5x-4))+c)} is e^c(x/(5x-4))^{5/4}