What is ln|sqrt(17)|-ln|16sqrt(17)| ?

The solution to ln|sqrt(17)|-ln|16sqrt(17)| is -4ln(2)

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simplify ln|sqrt(17)|-ln|16sqrt(17)|

simplify

ln 17 - ln 1617

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

ln 17 - ln 1617

Apply log rule:

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

ln 17 - ln 1617 = ln (\frac{17}{16 17})

= ln (\frac{17}{16 17})

\frac{17}{16 17} = \frac{1}{16}

= ln (\frac{1}{16})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= - ln (2^{4})

Apply log rule:

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

ln (2^{4}) = 4 ln (2)

= - 4 ln (2)

5 \cdot ln (\frac{0.47}{0.0094})

ln (\frac{2}{4}) \cdot 10

lo g_{10} (\frac{( x y ^{5} )}{z ^{5}})

2 ln (x - 2) - 2 ln (x)

ln (v) - ln (x - 1) - 2 ln (x)

What is ln|sqrt(17)|-ln|16sqrt(17)| ?
The solution to ln|sqrt(17)|-ln|16sqrt(17)| is -4ln(2)