What is 0.25*ln((10^{17}*10^{16})/((10^{10))^2}) ?

The solution to 0.25*ln((10^{17}*10^{16})/((10^{10))^2}) is 3.25ln(10)

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simplify 0.25ln((10^{17}10^{16})/((10^{10))^2})

simplify

0.25 \cdot ln (\frac{1 0 ^{17} \cdot 1 0 ^{16}}{( 1 0 ^{10} ) ^{2}})

3.25 ln (10)

Decimal Notation

7.48340 \dots

Solution steps

0.25 ln (\frac{1 0 ^{17} \cdot 1 0 ^{16}}{( 1 0 ^{10} ) ^{2}})

Apply log rule:

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

ln (\frac{1 0 ^{17} \cdot 1 0 ^{16}}{( 1 0 ^{10} ) ^{2}}) = ln (1 0^{17} \cdot 1 0^{16}) - ln ((1 0^{10})^{2})

= 0.25 (ln (1 0^{17} \cdot 1 0^{16}) - ln ((1 0^{10})^{2}))

Apply log rule:

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

ln ((1 0^{10})^{2}) = 2 ln (1 0^{10})

= 0.25 (ln (1 0^{17} \cdot 1 0^{16}) - 2 ln (1 0^{10}))

ln (1 0^{17} \cdot 1 0^{16}) = 33 ln (10)

2 ln (1 0^{10}) = 20 ln (10)

= 0.25 (33 ln (10) - 20 ln (10))

Add similar elements:

33 ln (10) - 20 ln (10) = 13 ln (10)

= 13 \cdot 0.25 ln (10)

Multiply the numbers:

0.25 \cdot 13 = 3.25

= 3.25 ln (10)

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lo g_{3} (\frac{21 x}{x - 1})

lo g_{8} (\frac{( ab ) ^{3}}{c ^{5}})

What is 0.25*ln((10^{17}*10^{16})/((10^{10))^2}) ?
The solution to 0.25*ln((10^{17}*10^{16})/((10^{10))^2}) is 3.25ln(10)