What is 5e^{ln(5)-ln(2)}-e^{2(ln(5)-ln(2))} ?

The solution to 5e^{ln(5)-ln(2)}-e^{2(ln(5)-ln(2))} is 25/4

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simplify 5e^{ln(5)-ln(2)}-e^{2(ln(5)-ln(2))}

simplify

5 e^{l n (5) - l n (2)} - e^{2 (l n (5) - l n (2))}

\frac{25}{4}

Decimal Notation

6.25

Solution steps

5 e^{l n (5) - l n (2)} - e^{2 (l n (5) - l n (2))}

Apply log rule:

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

ln (5) - ln (2) = ln (\frac{5}{2})

= 5 e^{l n (\frac{5}{2})} - e^{2 (l n (5) - l n (2))}

Apply log rule:

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

ln (5) - ln (2) = ln (\frac{5}{2})

= 5 e^{l n (\frac{5}{2})} - e^{2 l n (\frac{5}{2})}

5 e^{l n (\frac{5}{2})} = \frac{25}{2}

e^{2 l n (\frac{5}{2})} = \frac{5 ^{2}}{2 ^{2}}

= \frac{25}{2} - \frac{5 ^{2}}{2 ^{2}}

Simplify

= \frac{25}{4}

ln (\frac{2 x}{y ^{2}})

lo g_{e} (\frac{∣ x + 1 ∣ - 1}{∣ x - 3 ∣ + 1})

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

ln (\frac{13}{15})

lo g_{2} (\frac{4}{x + 9})

What is 5e^{ln(5)-ln(2)}-e^{2(ln(5)-ln(2))} ?
The solution to 5e^{ln(5)-ln(2)}-e^{2(ln(5)-ln(2))} is 25/4