What is 2.6ln|10|-2.6ln|5| ?

The solution to 2.6ln|10|-2.6ln|5| is ln(6.06286…)

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simplify 2.6ln|10|-2.6ln|5|

simplify

2.6 ln ∣ 10 ∣ - 2.6 ln ∣ 5 ∣

ln (6.06286 \dots)

Decimal Notation

1.80218 \dots

Solution steps

2.6 ln ∣ 10 ∣ - 2.6 ln ∣ 5 ∣

Apply log rule:

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

2.6 ln ∣ 10 ∣ = ln (∣ 10 ∣^{2.6})

= ln (∣ 10 ∣^{2.6}) - 2.6 ln ∣ 5 ∣

Apply log rule:

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

2.6 ln ∣ 5 ∣ = ln (∣ 5 ∣^{2.6})

= ln (∣ 10 ∣^{2.6}) - ln (∣ 5 ∣^{2.6})

Apply log rule:

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

ln (∣ 10 ∣^{2.6}) - ln (∣ 5 ∣^{2.6}) = ln (\frac{∣ 10 ∣ ^{2.6}}{∣ 5 ∣ ^{2.6}})

= ln (\frac{∣ 10 ∣ ^{2.6}}{∣ 5 ∣ ^{2.6}})

\frac{∣ 10 ∣ ^{2.6}}{∣ 5 ∣ ^{2.6}} = 6.06286 \dots

= ln (6.06286 \dots)

lo g_{e} (x) + lo g_{e} (x - 1)

92.45 + 20 lo g_{10} (12.5 \cdot 52)

- \frac{2 ln ( 3 )}{ln ( \frac{4}{3} )}

lo g_{7} (\frac{sin ( x ) \cdot cos ( x )}{e ^{x} \cdot 2 ^{x}})

\frac{\frac{l n ( 2 ) - l n ( 3 )}{l n ( 3 )}}{- 1}