What is 2ln|4|+3/4+3ln|5| ?

The solution to 2ln|4|+3/4+3ln|5| is ln(2000)+3/4

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simplify 2ln|4|+3/4+3ln|5|

simplify

2 ln ∣ 4 ∣ + \frac{3}{4} + 3 ln ∣ 5 ∣

ln (2000) + \frac{3}{4}

Decimal Notation

8.35090 \dots

Solution steps

2 ln ∣ 4 ∣ + \frac{3}{4} + 3 ln ∣ 5 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln ∣ 4 ∣ = ln (∣ 4 ∣^{2})

= ln (∣ 4 ∣^{2}) + \frac{3}{4} + 3 ln ∣ 5 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln ∣ 5 ∣ = ln (∣ 5 ∣^{3})

= ln (∣ 4 ∣^{2}) + \frac{3}{4} + ln (∣ 5 ∣^{3})

Apply log rule:

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

ln (∣ 4 ∣^{2}) + ln (∣ 5 ∣^{3}) = ln (∣ 5 ∣^{3} ∣ 4 ∣^{2})

= ln (∣ 5 ∣^{3} ∣ 4 ∣^{2}) + \frac{3}{4}

∣ 4 ∣^{2} ∣ 5 ∣^{3} = 2000

= ln (2000) + \frac{3}{4}

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