What is ln((0.75)/(0.691*10^{11)}) ?

The solution to ln((0.75)/(0.691*10^{11)}) is ln(0.75)-ln(0.691)-11ln(10)

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simplify ln((0.75)/(0.691*10^{11)})

simplify

ln (\frac{0.75}{0.691 \cdot 1 0 ^{11}})

ln (0.75) - ln (0.691) - 11 ln (10)

Decimal Notation

- 25.24650 \dots

Solution steps

ln (\frac{0.75}{0.691 \cdot 1 0 ^{11}})

Apply log rule:

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

ln (\frac{0.75}{0.691 \cdot 1 0 ^{11}}) = ln (0.75) - ln (0.691 \cdot 1 0^{11})

= ln (0.75) - ln (1 0^{11} \cdot 0.691)

Apply log rule:

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

ln (0.691 \cdot 1 0^{11}) = ln (0.691) + ln (1 0^{11})

= ln (0.75) - (ln (0.691) + ln (1 0^{11}))

Apply log rule:

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

ln (1 0^{11}) = 11 ln (10)

= ln (0.75) - (ln (0.691) + 11 ln (10))

- (ln (0.691) + 11 ln (10)) : - ln (0.691) - 11 ln (10)

= ln (0.75) - ln (0.691) - 11 ln (10)

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What is ln((0.75)/(0.691*10^{11)}) ?
The solution to ln((0.75)/(0.691*10^{11)}) is ln(0.75)-ln(0.691)-11ln(10)