What is ln(1/(e^8))+ln(8)e^3 ?

The solution to ln(1/(e^8))+ln(8)e^3 is 3e^3ln(2)-8

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simplify ln(1/(e^8))+ln(8)e^3

simplify

ln (\frac{1}{e ^{8}}) + ln (8) e^{3}

3 e^{3} ln (2) - 8

Decimal Notation

33.76669 \dots

Solution steps

ln (\frac{1}{e ^{8}}) + ln (8) e^{3}

Apply log rule:

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

ln (\frac{1}{e ^{8}}) = ln (1) - ln (e^{8})

= ln (1) - ln (e^{8}) + e^{3} ln (8)

Apply log rule:

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

ln (e^{8}) = 8 ln (e)

= ln (1) - 8 ln (e) + ln (8) e^{3}

ln (1) = 0

8 ln (e) = 8

= 0 - 8 + e^{3} ln (8)

Subtract the numbers:

0 - 8 = - 8

= e^{3} ln (8) - 8

Simplify

ln (8) : 3 ln (2)

= 3 e^{3} ln (2) - 8

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What is ln(1/(e^8))+ln(8)e^3 ?
The solution to ln(1/(e^8))+ln(8)e^3 is 3e^3ln(2)-8