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Popular >

simplify ln(4e^{6-t})

Solution

simplify

ln (4 e^{6 - t})

Solution

2 ln (2) + 6 - t

Solution steps

ln (4 e^{6 - t})

Apply log rule:

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

ln (4 e^{6 - t}) = ln (4) + ln (e^{6 - t})

= ln (4) + ln (e^{- t + 6})

Apply log rule:

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

ln (e^{6 - t}) = (6 - t) ln (e)

= ln (4) + (6 - t) ln (e)

(6 - t) ln (e) = 6 - t

= ln (4) + 6 - t

ln (4) = 2 ln (2)

= 2 ln (2) + 6 - t

Popular Examples

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2 ln (a) - ln (a^{2} + 1)

Frequently Asked Questions (FAQ)

What is ln(4e^{6-t}) ?
The solution to ln(4e^{6-t}) is 2ln(2)+6-t