What is 0.026*ln((0.4644)/(8*10^{-16)}) ?

The solution to 0.026*ln((0.4644)/(8*10^{-16)}) is 0.026(ln(0.4644)+ln(5^{16}*8192))

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simplify 0.026ln((0.4644)/(810^{-16)})

simplify

0.026 \cdot ln (\frac{0.4644}{8 \cdot 1 0 ^{- 16}})

0.026 (ln (0.4644) + ln (5^{16} \cdot 8192))

Decimal Notation

0.88386 \dots

Solution steps

0.026 ln (\frac{0.4644}{8 \cdot 1 0 ^{- 16}})

Apply log rule:

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

ln (\frac{0.4644}{8 \cdot 1 0 ^{- 16}}) = ln (0.4644) - ln (8 \cdot 1 0^{- 16})

= 0.026 (ln (0.4644) - ln (1 0^{- 16} \cdot 8))

Multiply

8 \cdot 1 0^{- 16} : \frac{1}{5 ^{16} \cdot 8192}

= 0.026 (ln (0.4644) - ln (\frac{1}{5 ^{16} \cdot 8192}))

Apply log rule:

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

= 0.026 (ln (0.4644) - (- ln (5^{16} \cdot 8192)))

Apply rule

- (- a) = a

= 0.026 (ln (0.4644) + ln (5^{16} \cdot 8192))

lo g_{10} (5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)

4 (lo g_{5} (y) - 2 lo g_{5} (z)) + 3 lo g_{5} (w)

ln (3) - ln (2) - 1

\frac{1}{2} ln (5 + 2) - \frac{1}{2} ln (5 + 0)

ln (\frac{1}{( 3.5 e ^{(- 4 T)} - 5 e ^{(- T)} + 2.5 )})

What is 0.026*ln((0.4644)/(8*10^{-16)}) ?
The solution to 0.026*ln((0.4644)/(8*10^{-16)}) is 0.026(ln(0.4644)+ln(5^{16}*8192))