What is ln(e^{36}-1)-ln(36e^{36}) ?

The solution to ln(e^{36}-1)-ln(36e^{36}) is ln(e^{36}-1)-2ln(6)-36

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simplify ln(e^{36}-1)-ln(36e^{36})

simplify

ln (e^{36} - 1) - ln (36 e^{36})

ln (e^{36} - 1) - 2 ln (6) - 36

Decimal Notation

- 3.58351 \dots

Solution steps

ln (e^{36} - 1) - ln (36 e^{36})

Apply log rule:

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

ln (36 e^{36}) = ln (36) + ln (e^{36})

= ln (e^{36} - 1) - (ln (36) + ln (e^{36}))

Apply log rule:

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

ln (e^{36}) = 36 ln (e)

= ln (e^{36} - 1) - (ln (36) + 36 ln (e))

- (ln (36) + 36 ln (e)) = - (2 ln (6) + 36)

= ln (e^{36} - 1) - (2 ln (6) + 36)

- (2 ln (6) + 36) : - 2 ln (6) - 36

= ln (e^{36} - 1) - 2 ln (6) - 36

ln (a) - 6 ln (b) + 5 ln (c)

4 lo g_{3} (X) - 2 lo g_{3} (Y)

lo g_{10} (x^{3} - 7 x + 6) - lo g_{10} (x^{2} + x - 6)

ln (2 \cdot 5)

10 lo g_{10} (\frac{108}{10 8 _{0}})

What is ln(e^{36}-1)-ln(36e^{36}) ?
The solution to ln(e^{36}-1)-ln(36e^{36}) is ln(e^{36}-1)-2ln(6)-36