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Popular >

simplify ln(3ln(e^e))

Solution

simplify

ln (3 ln (e^{e}))

Solution

ln (3) + 1

+1

Decimal Notation

2.09861 \dots

Solution steps

ln (3 ln (e^{e}))

Apply log rule:

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

ln (3 ln (e^{e})) = ln (3) + ln (ln (e^{e}))

= ln (3) + ln (ln (e^{e}))

Apply log rule:

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

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

= ln (3) + ln (e ln (e))

Apply log rule:

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

ln (e ln (e)) = ln (e) + ln (ln (e))

= ln (3) + ln (e) + ln (ln (e))

ln (e) = 1

ln (ln (e)) = 0

= ln (3) + 1 + 0

Add the numbers:

1 + 0 = 1

= ln (3) + 1

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Frequently Asked Questions (FAQ)

What is ln(3ln(e^e)) ?
The solution to ln(3ln(e^e)) is ln(3)+1