What is ln((10^{17})/(10^{18)}) ?

The solution to ln((10^{17})/(10^{18)}) is -ln(10)

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simplify ln((10^{17})/(10^{18)})

simplify

ln (\frac{1 0 ^{17}}{1 0 ^{18}})

- ln (10)

Decimal Notation

- 2.30258 \dots

Solution steps

ln (\frac{1 0 ^{17}}{1 0 ^{18}})

Apply log rule:

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

ln (\frac{1 0 ^{17}}{1 0 ^{18}}) = ln (1 0^{17}) - ln (1 0^{18})

= ln (1 0^{17}) - ln (1 0^{18})

Apply log rule:

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

ln (1 0^{17}) = 17 ln (10)

= 17 ln (10) - ln (1 0^{18})

Apply log rule:

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

ln (1 0^{18}) = 18 ln (10)

= 17 ln (10) - 18 ln (10)

Add similar elements:

17 ln (10) - 18 ln (10) = - ln (10)

= - ln (10)

- lo g_{10} (5.5 \cdot 1 0^{- 14})

ln (\frac{5 - 2 6}{2 - 3})

\frac{1}{2} ln (\frac{1}{2}) - \frac{1}{2}

- lo g_{10} (1 0^{- 14} \frac{1}{5.4 \cdot 1 0 ^{- 4}})

ln (4 x^{6} y^{8})

What is ln((10^{17})/(10^{18)}) ?
The solution to ln((10^{17})/(10^{18)}) is -ln(10)