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Popular >

simplify ln(5/7 e^{7t})

Solution

simplify

ln (\frac{5}{7} e^{7 t})

Solution

ln (5) - ln (7) + 7 t

Solution steps

ln (\frac{5}{7} e^{7 t})

Apply log rule:

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

ln (\frac{5}{7} e^{7 t}) = ln (\frac{5}{7}) + ln (e^{7 t})

= ln (\frac{5}{7}) + ln (e^{7 t})

Apply log rule:

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

ln (e^{7 t}) = 7 t ln (e)

= ln (\frac{5}{7}) + 7 t ln (e)

Apply log rule:

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

ln (\frac{5}{7}) = ln (5) - ln (7)

= ln (5) - ln (7) + 7 ln (e) t

7 t ln (e) = 7 t

= ln (5) - ln (7) + 7 t

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Frequently Asked Questions (FAQ)

What is ln(5/7 e^{7t}) ?
The solution to ln(5/7 e^{7t}) is ln(5)-ln(7)+7t