What is expand 2/7*ln|65-6|+5/7*ln|65+1| ?

The solution to expand 2/7*ln|65-6|+5/7*ln|65+1| is 1/7 ln(66^5*3481)

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expand 2/7ln|65-6|+5/7ln|65+1|

expand

\frac{2}{7} \cdot ln ∣ 65 - 6 ∣ + \frac{5}{7} \cdot ln ∣ 65 + 1 ∣

\frac{1}{7} ln (6 6^{5} \cdot 3481)

Decimal Notation

4.15762 \dots

Solution steps

\frac{2}{7} ln ∣ 65 - 6 ∣ + \frac{5}{7} ln ∣ 65 + 1 ∣

Apply log rule:

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

\frac{2}{7} ln ∣ 65 - 6 ∣ = ln (∣ 65 - 6 ∣^{\frac{2}{7}})

= ln (∣ 65 - 6 ∣^{\frac{2}{7}}) + \frac{5}{7} ln ∣ 65 + 1 ∣

Apply log rule:

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

\frac{5}{7} ln ∣ 65 + 1 ∣ = ln (∣ 65 + 1 ∣^{\frac{5}{7}})

= ln (∣ 65 - 6 ∣^{\frac{2}{7}}) + ln (∣ 65 + 1 ∣^{\frac{5}{7}})

Apply log rule:

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

ln (∣ 65 - 6 ∣^{\frac{2}{7}}) + ln (∣ 65 + 1 ∣^{\frac{5}{7}}) = ln (∣ 65 - 6 ∣^{\frac{2}{7}} ∣ 65 + 1 ∣^{\frac{5}{7}})

= ln (∣ 65 - 6 ∣^{\frac{2}{7}} ∣ 65 + 1 ∣^{\frac{5}{7}})

Expand

∣ 65 - 6 ∣^{\frac{2}{7}} ∣ 65 + 1 ∣^{\frac{5}{7}} : 5 9^{\frac{2}{7}} \cdot 6 6^{\frac{5}{7}}

= ln (5 9^{\frac{2}{7}} \cdot 6 6^{\frac{5}{7}})

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

Rewrite as

= ln ((5 9^{2} \cdot 6 6^{5})^{\frac{1}{7}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{7} ln (6 6^{5} \cdot 5 9^{2})

5 9^{2} = 3481

= \frac{1}{7} ln (6 6^{5} \cdot 3481)

5 \cdot lo g_{10} (x) - 3 \cdot lo g_{10} (y)

ln (\frac{2 d x}{x})

ln ((x) (x - 3))

- lo g_{10} (8 \cdot 1 0^{- 4})

3 lo g_{6} (x) - 2 lo g_{6} (y)

What is expand 2/7*ln|65-6|+5/7*ln|65+1| ?
The solution to expand 2/7*ln|65-6|+5/7*ln|65+1| is 1/7 ln(66^5*3481)