What is simplify-1/7 ln|100+6|+1/7 ln|100-1| ?

The solution to simplify-1/7 ln|100+6|+1/7 ln|100-1| is 1/7 ln(99/106)

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simplify-1/7 ln|100+6|+1/7 ln|100-1|

simplify

- \frac{1}{7} ln ∣ 100 + 6 ∣ + \frac{1}{7} ln ∣ 100 - 1 ∣

\frac{1}{7} ln (\frac{99}{106})

Decimal Notation

- 0.00975 \dots

Solution steps

- \frac{1}{7} ln ∣ 100 + 6 ∣ + \frac{1}{7} ln ∣ 100 - 1 ∣

Apply log rule:

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

\frac{1}{7} ln ∣ 100 + 6 ∣ = ln (∣ 100 + 6 ∣^{\frac{1}{7}})

= - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) + \frac{1}{7} ln ∣ 100 - 1 ∣

Apply log rule:

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

\frac{1}{7} ln ∣ 100 - 1 ∣ = ln (∣ 100 - 1 ∣^{\frac{1}{7}})

= - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) + ln (∣ 100 - 1 ∣^{\frac{1}{7}})

Apply log rule:

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

ln (∣ 100 - 1 ∣^{\frac{1}{7}}) - ln (∣ 100 + 6 ∣^{\frac{1}{7}}) = ln (\frac{∣ 100 - 1 ∣ ^{\frac{1}{7}}}{∣ 100 + 6 ∣ ^{\frac{1}{7}}})

= ln (\frac{∣ 100 - 1 ∣ ^{\frac{1}{7}}}{∣ 100 + 6 ∣ ^{\frac{1}{7}}})

Rewrite as

= ln ((\frac{99}{106})^{\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 (\frac{99}{106})

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What is simplify-1/7 ln|100+6|+1/7 ln|100-1| ?
The solution to simplify-1/7 ln|100+6|+1/7 ln|100-1| is 1/7 ln(99/106)