What is ln((|5.1-2|^2)/(|5.1-3|)) ?

The solution to ln((|5.1-2|^2)/(|5.1-3|)) is 2ln(3.1)-ln(2.1)

Popular >

simplify ln((|5.1-2|^2)/(|5.1-3|))

simplify

ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣})

2 ln (3.1) - ln (2.1)

Decimal Notation

1.52086 \dots

Solution steps

ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣})

Apply log rule:

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

ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣}) = ln (∣ 5.1 - 2 ∣^{2}) - ln ∣ 5.1 - 3 ∣

= ln (∣ 5.1 - 2 ∣^{2}) - ln ∣ 5.1 - 3 ∣

Apply log rule:

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

ln (∣ 5.1 - 2 ∣^{2}) = 2 ln ∣ 5.1 - 2 ∣

= 2 ln ∣ 5.1 - 2 ∣ - ln ∣ 5.1 - 3 ∣

2 ln ∣ 5.1 - 2 ∣ = 2 ln (3.1)

ln ∣ 5.1 - 3 ∣ = ln (2.1)

= 2 ln (3.1) - ln (2.1)

2 ln (3) + 3 ln (27) - 2 ln (9)

ln (\frac{16}{x ^{2}})

\frac{3}{2} \cdot ln (6)

ln (\frac{1}{3 ^{x}})

2 lo g_{10} (a) + lo g_{10} (b) - 3 lo g_{10} (c)

What is ln((|5.1-2|^2)/(|5.1-3|)) ?
The solution to ln((|5.1-2|^2)/(|5.1-3|)) is 2ln(3.1)-ln(2.1)