What is ln(|2+2|^{1.75}|2-3|^{0.25}|2|^2) ?

The solution to ln(|2+2|^{1.75}|2-3|^{0.25}|2|^2) is 5.5ln(2)

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simplify ln(|2+2|^{1.75}|2-3|^{0.25}|2|^2)

simplify

ln (∣ 2 + 2 ∣^{1.75} ∣ 2 - 3 ∣^{0.25} ∣ 2 ∣^{2})

5.5 ln (2)

Decimal Notation

3.81230 \dots

Solution steps

ln (∣ 2 + 2 ∣^{1.75} ∣ 2 - 3 ∣^{0.25} ∣ 2 ∣^{2})

Apply log rule:

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

ln (∣ 2 + 2 ∣^{1.75} ∣ 2 - 3 ∣^{0.25} ∣ 2 ∣^{2}) = ln (∣ 2 + 2 ∣^{1.75}) + ln (∣ 2 - 3 ∣^{0.25}) + ln (∣ 2 ∣^{2})

= ln (∣ 2 + 2 ∣^{1.75}) + ln (∣ 2 - 3 ∣^{0.25}) + ln (∣ 2 ∣^{2})

Apply log rule:

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

ln (∣ 2 + 2 ∣^{1.75}) = 1.75 ln ∣ 2 + 2 ∣

= 1.75 ln ∣ 2 + 2 ∣ + ln (∣ 2 - 3 ∣^{0.25}) + ln (∣ 2 ∣^{2})

Apply log rule:

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

ln (∣ 2 - 3 ∣^{0.25}) = 0.25 ln ∣ 2 - 3 ∣

= 1.75 ln ∣ 2 + 2 ∣ + 0.25 ln ∣ 2 - 3 ∣ + ln (∣ 2 ∣^{2})

Apply log rule:

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

ln (∣ 2 ∣^{2}) = 2 ln ∣ 2 ∣

= 1.75 ln ∣ 2 + 2 ∣ + 0.25 ln ∣ 2 - 3 ∣ + 2 ln ∣ 2 ∣

1.75 ln ∣ 2 + 2 ∣ = 1.75 ln (4)

0.25 ln ∣ 2 - 3 ∣ = 0

2 ln ∣ 2 ∣ = 2 ln (2)

= 1.75 ln (4) + 0 + 2 ln (2)

1.75 ln (4) + 0 + 2 ln (2) = 1.75 ln (4) + 2 ln (2)

= 2 ln (2) + 1.75 ln (4)

1.75 ln (4) = 3.5 ln (2)

= 2 ln (2) + 3.5 ln (2)

Add similar elements:

2 ln (2) + 3.5 ln (2) = 5.5 ln (2)

= 5.5 ln (2)

ln (2 \cdot \frac{5890}{5680})

lo g_{\frac{1}{2}} (2 e^{3})

ln (\frac{3}{2 e})

\frac{0.01 \cdot 2415}{π \cdot 0.003 \cdot 51271} \cdot ln (\frac{10}{60})

lo g_{\frac{1}{3}} (\frac{1}{6})

What is ln(|2+2|^{1.75}|2-3|^{0.25}|2|^2) ?
The solution to ln(|2+2|^{1.75}|2-3|^{0.25}|2|^2) is 5.5ln(2)