What is ln(sqrt(1+15)-1)-ln(sqrt(15)) ?

The solution to ln(sqrt(1+15)-1)-ln(sqrt(15)) is 1/2 ln(3/5)

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simplify ln(sqrt(1+15)-1)-ln(sqrt(15))

simplify

ln (1 + 15 - 1) - ln (15)

\frac{1}{2} ln (\frac{3}{5})

Decimal Notation

- 0.25541 \dots

Solution steps

ln (1 + 15 - 1) - ln (15)

Apply log rule:

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

ln (1 + 15 - 1) - ln (15) = ln (\frac{1 + 15 - 1}{15})

= ln (\frac{1 + 15 - 1}{15})

\frac{1 + 15 - 1}{15} = \frac{3}{5}

= ln (\frac{3}{5})

Rewrite as

= ln ((\frac{3}{5})^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} ln (\frac{3}{5})

ln (\frac{108}{162}) \cdot \frac{1}{- 0.01667}

- \frac{1}{2} ln (x) + ln (\frac{1}{x ^{2}})

ln (\frac{( \frac{0.296}{0.303} )}{9.9})

(ln (ln (3)) - ln (ln (2))) d x

2 lo g_{3^{^{'}}} (+ 4 lo g_{2^{^{'}}} (- 2 lo g_{1 2^{^{'}}} (x)))

What is ln(sqrt(1+15)-1)-ln(sqrt(15)) ?
The solution to ln(sqrt(1+15)-1)-ln(sqrt(15)) is 1/2 ln(3/5)