What is ln(25e^2*1/36) ?

The solution to ln(25e^2*1/36) is ln(25)+2ln(e)++ln(1)-ln(36)

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simplify ln(25e^2*1/36)

simplify

ln (25 e^{2} \cdot \frac{1}{36})

ln (25) + 2 ln (e) + + ln (1) - ln (36)

Decimal Notation

1.63535 \dots

Solution steps

ln (25 e^{2} \frac{1}{36})

Apply log rule:

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

ln (25 e^{2} \frac{1}{36}) = ln (25) + ln (e^{2}) + ln (\frac{1}{36})

= ln (25) + ln (e^{2}) + ln (\frac{1}{36})

Apply log rule:

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

ln (e^{2}) = 2 ln (e)

= ln (25) + 2 ln (e) + ln (\frac{1}{36})

Apply log rule:

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

ln (\frac{1}{36}) = ln (1) - ln (36)

= ln (25) + 2 ln (e) + + ln (1) - ln (36)

ln (x^{4}) - ln (x)

lo g_{5} (4) - lo g_{5} (9)

lo g_{m} (\frac{67}{83})

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

What is ln(25e^2*1/36) ?
The solution to ln(25e^2*1/36) is ln(25)+2ln(e)++ln(1)-ln(36)