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Popular >

simplify ln(1/10)+ln(e^3)

Solution

simplify

ln (\frac{1}{10}) + ln (e^{3})

Solution

- ln (10) + 3

+1

Decimal Notation

0.69741 \dots

Solution steps

ln (\frac{1}{10}) + ln (e^{3})

Apply log rule:

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

ln (\frac{1}{10}) = ln (1) - ln (10)

= ln (1) - ln (10) + ln (e^{3})

Apply log rule:

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

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

= ln (1) - ln (10) + 3 ln (e)

ln (1) = 0

3 ln (e) = 3

= 0 - ln (10) + 3

Add the numbers:

0 + 3 = 3

= - ln (10) + 3

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Frequently Asked Questions (FAQ)

What is ln(1/10)+ln(e^3) ?
The solution to ln(1/10)+ln(e^3) is -ln(10)+3